Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Easy2 minPYQ_2017

MathematicsEasysingle choice

Let $z \in C,$ the set of complex numbers. Then the equation, $2 |z + 3 i| - |z - i| = 0$ represents:

Options:

Answer:

Solution:

Let $z = x + i y$ so that

$2 |x + i (y + 3)| = |x + i (y - 1)|$

$\Rightarrow 2 \sqrt{x^{2} + {(y + 3)}^{2}} = \sqrt{x^{2} + {(y - 1)}^{2}}$

$\Rightarrow 4 x^{2} + 4 {(y + 3)}^{2} = x^{2} + {(y - 1)}^{2}$

$\Rightarrow 3 x^{2} + 3 y^{2} +26 y + 35 = 0$

$\Rightarrow x^{2} + y^{2} + \frac{26}{3} y + \frac{35}{3} = 0$

$\Rightarrow r = \sqrt{0 + \frac{169}{9} - \frac{35}{3}}$

$\Rightarrow r = \sqrt{\frac{64}{9}} = \frac{8}{3}$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2017

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