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Question

If z and ω be two non-zero compex numbers such that |z|=|ω| and arg(z)+arg(ω)=π, then z equals

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
Since |z|=|ω| and arg(z)=πarg(ω)
Let ω=reiθ, then ¯¯¯ω=reiθz=rei(πθ)=r eiπ.eiθ=reiθ=¯¯¯ω

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