If z is a complex number such that z 2 = ( ¯ z ) 2 ,then Options: A . &nbsp z is purely real B . &nbsp z is purely imaginary C . &nbsp Either z is purely real or purely imaginary D . &nbsp None of these

If z is a complex number such that z2 = (¯z)2,then

Question -

If z is a complex number such that $z^{2}$ = ( $¯ z)^{2}$ ,then

Options:

A . z is purely real

B . z is purely imaginary

C . Either z is purely real or purely imaginary

D . None of these

Answer: Option C
:
C

Let z = x+iy, then its coonjucate $¯ z$ = x-iy

Given that $z^{2} = (¯ z)^{2}$

⇒ $x^{2}$ - $y^{2}$ + 2ixy = $x^{2}$ - $y^{2}$ - 2ixy ⇒ 4ixy = 0

if x ≠ 0 then y = 0 and if y ≠ 0 then x = 0

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