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Question

Let z and ω are two non-zero complex numbers such that |z|=|ω| and argz+argω=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 B ¯¯¯ω
Fromthehelpofgivenquestionz=|z|(cosθ+isinθ)whereθ=zIfθ1=wthentanθ=πθ1So,z=|w|(cos(πθ1)+isin(πθ1))=|w|(cosθ1+isinθ1)=|w|(cosθ1isinθ1)=¯¯¯¯w
Hence, option D is the correct answer.

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