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Question

Let z & w be two non zero complex numbers such that |z|=|w| and Argz+Argw=π, then z equals

A
w
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B
-w
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C
¯¯¯¯w
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D
¯¯¯¯w
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Solution

The correct option is D ¯¯¯¯w
Let
w=cosθ+isinθ

¯¯¯¯w=cosθisinθ

Now arg(z)=πarg(w)

z=cos(πθ)+isin(πθ)

=cos(θ)+isin(θ)

=¯¯¯¯w

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