Let z = x + iy be a non-zero complex number such that z 2 = i z 2 , where i = - 1 , then z lies on the :

x + i y 2 = i x 2 + y 2 ⇒ x 2 - y 2 + 2 i x y = i ( x 2 + y 2 ) compare real and imaginary parts ⇒ x = y

Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Easy2 minPYQ_2020

MathematicsEasysingle choice

Let $z = x + iy$ be a non-zero complex number such that $z^{2} = i {|z|}^{2}$ , where $i = \sqrt{- 1}$ , then $z$ lies on the :

Answer:

Solution:

${(x + i y)}^{2} = i (x^{2} + y^{2})$

$\Rightarrow x^{2} - y^{2} + 2 i x y = i (x^{2} + y^{2})$

compare real and imaginary parts

$\Rightarrow x = y$

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

⏱ 2mℹ️ Source: PYQ_2020

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