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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 conjugate \bar{z} = x - iy
Given that z2=(¯z)2
x2y2+2ixy=x2y22ixy 4ixy=0
If x then y = 0and if y 0 then x = 0


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