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z and ω are two non zero complex numbers such that |z|=|ω| and Arg z+Arg ω=π then z equals

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a

ω¯

b

−ω¯

c

ω

d

−ω

answer is B.

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Detailed Solution

Let |z|=|ω|=r ∴z=reiθ,ω=reiϕ , where θ+ϕ=π ( ∵ω¯=re−iϕ) ∴z=rei(π−ϕ)=reiπ.e−iϕ=−re−iϕ=−ω¯

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