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Question

Let z and ω are two non-zero complex numbers such that |z|=|ω| and arg z+arg ω=π, then z equal to

A
ω
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B
ω
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C
¯¯¯ω
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D
¯¯¯ω
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Solution

The correct option is D ¯¯¯ω
w=|w|eiθ
=|w|[cosθ+isinθ]
z=|w|ei(πθ)
=|w|[cosθ+isinθ]
=|w|[cosθisinθ]
=¯w

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