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=π−θ1So,z=|w|(cos(π−θ1)+isin(π−θ1))=|w|(−cosθ1+isinθ1)=−|w|(cosθ1−isinθ1)=−¯¯¯¯w