Mathematics › Complex Number
Complex Number Questions
345 questions across 10 subtopics — with step-by-step solutions.
(1)
Cube Root of Unity(25)
- If the cube roots of unity are then the ro... | Mathematics | TestHub
- If , where is a complex number, then the v... | Mathematics | TestHub
- Let and be non-zero complex numbers such t... | Mathematics | TestHub
- If is a cube root of unity, and . Then equals | Mathematics | TestHub
- Paragraph:Let , b and be three real number... | Mathematics | TestHub
- If then the value of is | Mathematics | TestHub
- If and are the roots of then the equation... | Mathematics | TestHub
- Ifare the distinct roots of the equationth... | Mathematics | TestHub
- Ifthenis equal to: | Mathematics | TestHub
- Letbe a root of quadratic equation,If, the... | Mathematics | TestHub
- Letbe a cube root of unity. Then the minim... | Mathematics | TestHub
- Ifandare real numbers such that, where, th... | Mathematics | TestHub
- The value ofis : | Mathematics | TestHub
- Let. Ifand, thenand, are the roots of the... | Mathematics | TestHub
- Ifandare two polynomials such that the pol... | Mathematics | TestHub
- Let. Then the value ofis______. | Mathematics | TestHub
- If, thenis equal to _____. | Mathematics | TestHub
- Ifis a complex number, then the number of... | Mathematics | TestHub
- Ifsatisfies the equationand, thenis equal to | Mathematics | TestHub
- For a non-zero complex number , let denote... | Mathematics | TestHub
- Let integers be such that . Then the numbe... | Mathematics | TestHub
- If is a root of the equation and , then n... | Mathematics | TestHub
- Let w \neq 1 be a cube root of unity. Poss... | Mathematics | TestHub
- Let 1, w, w^{2} be the cube root of unity.... | Mathematics | TestHub
- Consider two equations z^{3}=k^{3} List -... | Mathematics | TestHub
De-Moivres theorem(20)
- Ifandare two complex numbers such thatand,... | Mathematics | TestHub
- The value ofis | Mathematics | TestHub
- Ifthenandare roots of the equation : | Mathematics | TestHub
- Ifandare two complex numbers such thatand,... | Mathematics | TestHub
- Let a complex number be. Let another compl... | Mathematics | TestHub
- Let If and be the greatest integral part o... | Mathematics | TestHub
- If the real part of the complex numberisfo... | Mathematics | TestHub
- Letand,. Then,andare roots of the equation. | Mathematics | TestHub
- The value ofis | Mathematics | TestHub
- The complex numberis equal to: | Mathematics | TestHub
- Letandrespectively be the modulus and ampl... | Mathematics | TestHub
- Letbe the roots of the equationsuch that.... | Mathematics | TestHub
- Letbe the roots of the equationwith. Theni... | Mathematics | TestHub
- If 2^{7} \cos ^{3} \theta \cdot \sin ^{5}... | Mathematics | TestHub
- If \alpha_{1}, \alpha_{2}, \alpha_{3}, \al... | Mathematics | TestHub
- If Z=\frac{1}{2}(\sqrt{3}-i) then the leas... | Mathematics | TestHub
- Let 1, w, w^{2} be the cube root of unity.... | Mathematics | TestHub
- Match the solutions of the equation of Lis... | Mathematics | TestHub
- Let C=\cos \frac{2 \pi}{7}+\cos \frac{4 \p... | Mathematics | TestHub
- If \alpha_{1}, \alpha_{2}, \alpha_{3}, \al... | Mathematics | TestHub
General(Modulus,Argument,Conjugate)(161)
- If , its solution is given by | Mathematics | TestHub
- and are two non zero complex no.s such tha... | Mathematics | TestHub
- If and are two non-zero complex numbers su... | Mathematics | TestHub
- If then | Mathematics | TestHub
- Let , be complex numbers such that and . T... | Mathematics | TestHub
- If and , then is equal to | Mathematics | TestHub
- If and , then lies on | Mathematics | TestHub
- If and are two non-zero complex numbers su... | Mathematics | TestHub
- If , where and satisfies the condition tha... | Mathematics | TestHub
- Paragraph:Let be three sets of complex num... | Mathematics | TestHub
- The conjugate of a complex number is . The... | Mathematics | TestHub
- Paragraph:Let be three sets of complex num... | Mathematics | TestHub
- For the equation , if the product of roots... | Mathematics | TestHub
- Let be a complex number, where and are int... | Mathematics | TestHub
- If , then the maximum value of is equal to | Mathematics | TestHub
- Let be the complex number . Then the numbe... | Mathematics | TestHub
- Match the statements of Column I with thes... | Mathematics | TestHub
- The number of complex numbers such that eq... | Mathematics | TestHub
- Let and be two distinct complex numbers an... | Mathematics | TestHub
- The roots of the equation are | Mathematics | TestHub
- Let be real and be a complex number. If ha... | Mathematics | TestHub
- If is any complex number satisfying , then... | Mathematics | TestHub
- If and then | Mathematics | TestHub
- Let and be any two complex number. Stateme... | Mathematics | TestHub
- The amplitude of | Mathematics | TestHub
- Let be a complex number such that the imag... | Mathematics | TestHub
- Let and be complex numbers such that , and... | Mathematics | TestHub
- is equal to | Mathematics | TestHub
- Let , where is any non-zero complex number... | Mathematics | TestHub
- Let satisfy and . Statement is a real numb... | Mathematics | TestHub
- Ifis a complex number of unit modulus and... | Mathematics | TestHub
- If a complex number statisfies the equatio... | Mathematics | TestHub
- If and be two complex numbers such that is... | Mathematics | TestHub
- Let be any complex number such that is a p... | Mathematics | TestHub
- If then where is equal to | Mathematics | TestHub
- For all complex numbersof the formifthen | Mathematics | TestHub
- If and are 2 pairs of complex conjugate nu... | Mathematics | TestHub
- Letbe a complex number. Then, the set of a... | Mathematics | TestHub
- Ifis one of the roots of the equationthen... | Mathematics | TestHub
- The root of the equation which has greater... | Mathematics | TestHub
- Ifis a non-real complex number, then the m... | Mathematics | TestHub
- Let, be a complex number,, such thatis a r... | Mathematics | TestHub
- A value offor whichis purely imaginary, is | Mathematics | TestHub
- If and , then the complex number lies in t... | Mathematics | TestHub
- Ifsatisfies, then | Mathematics | TestHub
- Letthe set of complex numbers. Then the eq... | Mathematics | TestHub
- Letandbe real numbers such thatand. If the... | Mathematics | TestHub
- Letbe a complex number such thatwhere. IfT... | Mathematics | TestHub
- The equationrepresents a part of a circle... | Mathematics | TestHub
- The set of all , for which is a purely ima... | Mathematics | TestHub
- If then the difference between the greates... | Mathematics | TestHub
- Letbe non-zero complex numbers andbe the s... | Mathematics | TestHub
- The set of all, for whichis a purely imagi... | Mathematics | TestHub
- The least positive integerfor whichis | Mathematics | TestHub
- For a non-zero complex number, let argdeno... | Mathematics | TestHub
- Letwithand it satisfiesfor some natural nu... | Mathematics | TestHub
- Ifis a purely imaginary number and, then a... | Mathematics | TestHub
- Ifand, has magnitude, thenis equal to: | Mathematics | TestHub
- Ifandrepresents adjacent vertices of a reg... | Mathematics | TestHub
- LetThen the sum of the elements inis: | Mathematics | TestHub
- Letandbe any two non-zero complex numbers... | Mathematics | TestHub
- Let be a complex number such that where Th... | Mathematics | TestHub
- LetIfandrespectively denote the real and i... | Mathematics | TestHub
- Let where and are real numbers then equals | Mathematics | TestHub
- The value offor which the lociandon the ar... | Mathematics | TestHub
- Letbe a non-zero complex number such that,... | Mathematics | TestHub
- If the four complex numbersandrepresent th... | Mathematics | TestHub
- If then the value of is, | Mathematics | TestHub
- Ifis a real number, then an argument ofis | Mathematics | TestHub
- If the equationhas conjugate complex roots... | Mathematics | TestHub
- For a complex number, letdenote the real p... | Mathematics | TestHub
- Letand. If the curve represented byinterse... | Mathematics | TestHub
- If are complex numbers such that and and ,... | Mathematics | TestHub
- The region represented byis also given by... | Mathematics | TestHub
- Ifwherethen the pointlies on a | Mathematics | TestHub
- Letbe positive valued angles (in radian) s... | Mathematics | TestHub
- then is equal to . Value of is | Mathematics | TestHub
- If is a complex number such that , then | Mathematics | TestHub
- If the least and the largest real values o... | Mathematics | TestHub
- Ifis a complex number such thatis purely i... | Mathematics | TestHub
- The least value of where is complex number... | Mathematics | TestHub
- If the real part of the complex numberis z... | Mathematics | TestHub
- Letdenote the number of solutions of the e... | Mathematics | TestHub
- Letandbe two complex numbers such thatands... | Mathematics | TestHub
- Let a complex number, satisfy. Then, the l... | Mathematics | TestHub
- If , then the set of points is contained i... | Mathematics | TestHub
- The smallest positive integral value of su... | Mathematics | TestHub
- Letandbe the roots of the equation. Then,... | Mathematics | TestHub
- Letbe the set of all, for which the comple... | Mathematics | TestHub
- Letandbe two complex numbers such thatand,... | Mathematics | TestHub
- Let the minimum valueof,is attained at. Th... | Mathematics | TestHub
- Sum of squares of modulus of all the compl... | Mathematics | TestHub
- Forif the minimum value ofis, then a value... | Mathematics | TestHub
- Letdenote the complex conjugate of a compl... | Mathematics | TestHub
- Letdenote the complex conjugate of a compl... | Mathematics | TestHub
- Letbe complex numbers satisfying. Then the... | Mathematics | TestHub
- Let. Thenis equal to _______. | Mathematics | TestHub
- Letbe a complex number with non-zero imagi... | Mathematics | TestHub
- Let for some real numbersand. If the syste... | Mathematics | TestHub
- If, thenis equal to: | Mathematics | TestHub
- Let. Thenis equal to | Mathematics | TestHub
- For two non-zero complex number and , if a... | Mathematics | TestHub
- If forthenandare the roots of the equation | Mathematics | TestHub
- Letbe the point obtained by the rotation o... | Mathematics | TestHub
- Let be two non-zero real numbers. Then the... | Mathematics | TestHub
- Let be a complex number satisfying , where... | Mathematics | TestHub
- For, letand. Then among the two statements... | Mathematics | TestHub
- Let. Ifcontains exactly one positive integ... | Mathematics | TestHub
- If the setis equal to the interval, thenis... | Mathematics | TestHub
- LetandThenis equal to | Mathematics | TestHub
- Let the complex numberbe such thatis purel... | Mathematics | TestHub
- Let is a real number . Then which of the f... | Mathematics | TestHub
- Letbe two real numbers such that. If the c... | Mathematics | TestHub
- Let . , then is equal to | Mathematics | TestHub
- The modulus of is | Mathematics | TestHub
- LetThen the sum of the elements is inis | Mathematics | TestHub
- If are complex numbers such that , then is... | Mathematics | TestHub
- The sum of all possible values of , for wh... | Mathematics | TestHub
- Let and . Then the area of the region is : | Mathematics | TestHub
- The modulus of the complex number such tha... | Mathematics | TestHub
- Consider the following two statements : St... | Mathematics | TestHub
- Ifis a complex number such that, then the... | Mathematics | TestHub
- Let be a complex number such that and . Th... | Mathematics | TestHub
- Let be a complex number such that the real... | Mathematics | TestHub
- Letandbe two complex number such thatand.... | Mathematics | TestHub
- Let and be the sum and the product of all... | Mathematics | TestHub
- The sum of the square of the modulus of th... | Mathematics | TestHub
- Ifdenotes the number of solutions ofand, w... | Mathematics | TestHub
- If, is such thatandthenis equal to | Mathematics | TestHub
- If and 4 , then absolute value of equals | Mathematics | TestHub
- The area (in sq. units) of the region is | Mathematics | TestHub
- If, satisfies the equation, thenis equal to : | Mathematics | TestHub
- Let be the origin, the point be , the poin... | Mathematics | TestHub
- Let Then is equal to | Mathematics | TestHub
- If and are the roots of , then is equal to : | Mathematics | TestHub
- The number of complex numbers , satisfying... | Mathematics | TestHub
- If and are the roots of the equation , whe... | Mathematics | TestHub
- Let and be three complex numbers on the ci... | Mathematics | TestHub
- Among the statements(S1) : The set and is... | Mathematics | TestHub
- Let , be the equation of a circle with cen... | Mathematics | TestHub
- Let be the origin, the point be , the poin... | Mathematics | TestHub
- The number of complex numbers , satisfying... | Mathematics | TestHub
- Let Then is equal to | Mathematics | TestHub
- Let be such that . Then the sum of all pos... | Mathematics | TestHub
- Let and . Then the minimum value of is : | Mathematics | TestHub
- Let the product of and be , . Let p and q... | Mathematics | TestHub
- Let be the roots of the equation with . Le... | Mathematics | TestHub
- Let be a complex number such that . If , t... | Mathematics | TestHub
- If the complex number Z satisfying Z+|Z|=2... | Mathematics | TestHub
- The complex numbers sin x + i cos 2 x & co... | Mathematics | TestHub
- If z_{1} and z_{2} are two complex numbers... | Mathematics | TestHub
- Match List - I with List - IILIST ILIST II... | Mathematics | TestHub
- If z is a complex number satisfying z^{4}+... | Mathematics | TestHub
- If (1+\mathrm{i})(1+2 \mathrm{i})(1+3 \mat... | Mathematics | TestHub
- If z=(1+\sqrt{3} i)^{10}+(1-\sqrt{3} i)^{1... | Mathematics | TestHub
- If Z_{n}=\left(\cos \left(\frac{\pi}{n(n+1... | Mathematics | TestHub
- Let \mathrm{w}=\frac{\mathrm{z}^{2}-3 \mat... | Mathematics | TestHub
- Let be two complex numbers ( \mathrm{r}_{1... | Mathematics | TestHub
- If \frac{3 i z_{2}}{5 z_{1}} is purely rea... | Mathematics | TestHub
- If (a+i b)^{5}=\alpha+i \beta then (b+i a)... | Mathematics | TestHub
- If \left|z_{1}\right|=2,\left|z_{2}\right|... | Mathematics | TestHub
Geometric Application(107)
- The locus of the centre of a circle which... | Mathematics | TestHub
- Let and be two roots of the equation being... | Mathematics | TestHub
- If , then lies on | Mathematics | TestHub
- If , then the maximum value of is | Mathematics | TestHub
- If and , then all the values of lie on | Mathematics | TestHub
- A man walks a distance of 3 units from the... | Mathematics | TestHub
- Paragraph:Let be three sets of complex num... | Mathematics | TestHub
- The area of the triangle whose vertices ar... | Mathematics | TestHub
- If and is real, then the point represented... | Mathematics | TestHub
- Letand.Furtherand, where C is the set of a... | Mathematics | TestHub
- Let complex numbers α andlie on circlesand... | Mathematics | TestHub
- If the real part of is then the locus of t... | Mathematics | TestHub
- Ifis a complex number such thatthen the mi... | Mathematics | TestHub
- The complex number which satisfies the equ... | Mathematics | TestHub
- The largest value of, for which the region... | Mathematics | TestHub
- If complex number and 0 are vertices of eq... | Mathematics | TestHub
- A complex numberis said to be unimodular i... | Mathematics | TestHub
- Letand. SupposewhereIfandthenlies on | Mathematics | TestHub
- The point represented byin the Argand plan... | Mathematics | TestHub
- Ifandrepresent the vertices of an equilate... | Mathematics | TestHub
- Letbe the set of all complex numberssatisf... | Mathematics | TestHub
- All the points in the setlie on a | Mathematics | TestHub
- Letandbe two complex numbers satisfyingand... | Mathematics | TestHub
- Letbe such thatIfthen: | Mathematics | TestHub
- The equationrepresents: | Mathematics | TestHub
- Ifis a complex number satisfyingthencannot be | Mathematics | TestHub
- Letbe a complex number such thatand. Then,... | Mathematics | TestHub
- If the equationrepresents a circle wherear... | Mathematics | TestHub
- Letbe the roots of the equationandform an... | Mathematics | TestHub
- A pointmoves in the complex plane such tha... | Mathematics | TestHub
- Let and be three sets defined as andThen,... | Mathematics | TestHub
- Let be the set of all complex numbers. Let... | Mathematics | TestHub
- Letbe those complex numbers which satisfya... | Mathematics | TestHub
- If, then | Mathematics | TestHub
- For any complex number, let, where. Letand... | Mathematics | TestHub
- Letbe the set of all complex numbers. Leta... | Mathematics | TestHub
- The equationrepresents a circle with: | Mathematics | TestHub
- Letandbe two complex numbers such thatandh... | Mathematics | TestHub
- The area of the triangle with verticesandis | Mathematics | TestHub
- The equation of a circle iswhereA line whi... | Mathematics | TestHub
- Let the linesand(here) be normal to a circ... | Mathematics | TestHub
- If for the complex numberssatisfying, the... | Mathematics | TestHub
- Letrepresent the principal argument of the... | Mathematics | TestHub
- The number of elements in the set {and} is... | Mathematics | TestHub
- Letand. Then, | Mathematics | TestHub
- Ifsatisfiesand, then | Mathematics | TestHub
- The area of the polygon, whose vertices ar... | Mathematics | TestHub
- Letand. Thenis | Mathematics | TestHub
- Let. Then the set of all values of, for wh... | Mathematics | TestHub
- The number of points of intersectionandis | Mathematics | TestHub
- Let. Letattains minimum and maximum values... | Mathematics | TestHub
- For, letand. Then the number of elements i... | Mathematics | TestHub
- Let a circlein complex plane pass through... | Mathematics | TestHub
- LetandThen, forand, the least value ofis | Mathematics | TestHub
- Letbe the origin andbe the point. Ifis the... | Mathematics | TestHub
- Let{and}. Ifis the point inwhich is closes... | Mathematics | TestHub
- Let . Let be the circle of radius in the f... | Mathematics | TestHub
- If the center and radius of the circleare... | Mathematics | TestHub
- Let and Then, is equal to ________ | Mathematics | TestHub
- For all on the curve , let the locus of th... | Mathematics | TestHub
- Letbe a complex number such that. Thenlies... | Mathematics | TestHub
- Let and . The set represents a | Mathematics | TestHub
- For and , if is the radius of the circle t... | Mathematics | TestHub
- Let be the circle in the complex plane wit... | Mathematics | TestHub
- Letand. Let inbe maximum and minimum atand... | Mathematics | TestHub
- The points represented by the complex numb... | Mathematics | TestHub
- If forms a rectangle of area square units,... | Mathematics | TestHub
- Let. Letbe such thatand. Thenequals: | Mathematics | TestHub
- If are two distinct complex number such th... | Mathematics | TestHub
- If the locus of , such thatis a circle of... | Mathematics | TestHub
- Let be a complex number such that . If , t... | Mathematics | TestHub
- Let , be the equation of a circle with cen... | Mathematics | TestHub
- Let the curve , divide the region into two... | Mathematics | TestHub
- Let and . Then the minimum value of is : | Mathematics | TestHub
- If are the vertices of an equilateral tria... | Mathematics | TestHub
- The complex number \mathrm{a}+\mathrm{i},... | Mathematics | TestHub
- If |z-3 i|=3 , (where \mathrm{i}=\sqrt{-1}... | Mathematics | TestHub
- If Z -lies on the circle |z-2 i|=2 \sqrt{2... | Mathematics | TestHub
- If the imaginary part of the expression \f... | Mathematics | TestHub
- If |Z+2-i|=5 then maximum value of |3 Z+9-... | Mathematics | TestHub
- If |2 z-4-2 i|=|z| \sin \left(\frac{\pi}{4... | Mathematics | TestHub
- If z_{1}, z_{2}, z_{3} and z_{4} be the co... | Mathematics | TestHub
- The complex number 3+4 i is rotated about... | Mathematics | TestHub
- Find the least +ve integral value of ' a '... | Mathematics | TestHub
- The sum of the real parts of the complex n... | Mathematics | TestHub
- There are two complex numbers z such that... | Mathematics | TestHub
- Let \mathrm{z}_{1} and \mathrm{z}_{2} be t... | Mathematics | TestHub
- If z_{1}, z_{2} and z_{3} are the vertices... | Mathematics | TestHub
- If a complex number z satisfies |z-8-4 i|+... | Mathematics | TestHub
- Let \mathrm{A}, \mathrm{B}, \mathrm{C} be... | Mathematics | TestHub
- A triangle with vertices represented by z_... | Mathematics | TestHub
- Let \mathrm{A}_{1}, \mathrm{~A}_{2} \ldots... | Mathematics | TestHub
- The point of intersection of the curves \a... | Mathematics | TestHub
- Two lines \mathrm{zi}-\overline{\mathrm{z}... | Mathematics | TestHub
- If the argument of (z-a)(\bar{z}-b) is equ... | Mathematics | TestHub
- If \left|Z_{1}-Z_{2}\right|=\sqrt{25-12 \s... | Mathematics | TestHub
- In the Argand plane, let A(a) and B(b) be... | Mathematics | TestHub
- Let \mathrm{A}_{1}\left(\mathrm{Z}_{1}\rig... | Mathematics | TestHub
- If z \in C such that |z-1-3 i|+|z+1-3 i|=6... | Mathematics | TestHub
- Match the equation given in List-I to the... | Mathematics | TestHub
- Given \mathrm{f}(\mathrm{z})=\mathrm{z}^{2... | Mathematics | TestHub
- If \left|z_{i}\right|=12, i=1,2,3,4,5 and... | Mathematics | TestHub
- Two lines z i-\bar{z} i+2=0 and z(1+i)+\ba... | Mathematics | TestHub
- Let \lambda, z_{0} be two complex numbers.... | Mathematics | TestHub
- Number of points denoting the complex numb... | Mathematics | TestHub
- If z_{1}, z_{2}, z_{3} are non-zero comple... | Mathematics | TestHub
- The point of intersection of the curves \a... | Mathematics | TestHub
Locus Based on Distance Formula(4)
Miscellaneous/Mixed(11)
- A particle starts from the point , where .... | Mathematics | TestHub
- Let . Then, the value of at is | Mathematics | TestHub
- Letbe the set of all complex numberssatisf... | Mathematics | TestHub
- Let , and . Then which of the following st... | Mathematics | TestHub
- Let Z be a complex number given by, Z=\lef... | Mathematics | TestHub
- If z_{1}, z_{2}, z_{3}, \ldots \ldots ., z... | Mathematics | TestHub
- Value of \cot ^{2} \frac{\pi}{7}+\cot ^{2}... | Mathematics | TestHub
- The complex number z satisfying |z+2+i|+|z... | Mathematics | TestHub
- Match the following List-I with List-IILis... | Mathematics | TestHub
- The roots of the equation z^{5}+z^{6}+\ldo... | Mathematics | TestHub
- If \cos \alpha+\cos \beta+\cos \gamma=0=\s... | Mathematics | TestHub
Power of iota(5)
- when simplified has the value | Mathematics | TestHub
- Ifandbe the roots of the equationthen the... | Mathematics | TestHub
- Ifthen the greatest common divisor of the... | Mathematics | TestHub
- The least positive integersuch thatis a po... | Mathematics | TestHub
- , when simplified has the value | Mathematics | TestHub
Properties of Complex number(2)
nth roots of unity(9)
- Let List – I List – II(A)For each there ex... | Mathematics | TestHub
- For any integerletThe value of the express... | Mathematics | TestHub
- Theroots of unity are in | Mathematics | TestHub
- Ifare the roots of the equation, thenis eq... | Mathematics | TestHub
- Letbe the vertices of a regular octagon th... | Mathematics | TestHub
- Suppose that w is the imaginary (2009)^{\t... | Mathematics | TestHub
- If \alpha=\mathrm{e}^{\mathrm{i} 2 \pi / 7... | Mathematics | TestHub
- \quad \sum_{j=1}^{n-1} \frac{1}{1-e^{\frac... | Mathematics | TestHub
- Let \alpha=e^{\frac{i 2 \pi}{11}} and \lam... | Mathematics | TestHub
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