Question
If z and ω be two non-zero compex numbers such that |z|=|ω| and arg(z) + arg(ω)=π, then z equals
Answer: Option D
:
D
Since |z|=|ω| and arg(z)=π−arg(ω)
Let ω=reiθ, then ¯¯¯ω=re−iθ∴z=rei(π−θ)=reiπ.e−iθ=−re−iθ=−¯¯¯ω
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:
D
Since |z|=|ω| and arg(z)=π−arg(ω)
Let ω=reiθ, then ¯¯¯ω=re−iθ∴z=rei(π−θ)=reiπ.e−iθ=−re−iθ=−¯¯¯ω
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