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 :

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 :

line, $y = - x$
imaginary axis
line, $y = x$
real axis

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

$\Rightarrow x = y$

Asked in: JEE Main 2020 (06 Sep Shift 2)

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