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Question

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


A

z is purely real

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B

z is purely imaginary

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C

Either z is purely real or purely imaginary

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D

None of these

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Solution

The correct option is C

Either z is purely real or purely imaginary


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

Given that z2=(¯z)2

x2 - y2 + 2ixy = x2 - y2 - 2ixy ⇒ 4ixy = 0

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


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