Math miscellaneousHard

Question

z and w are two non zero complex no.s such that |z| = |w| and Arg z + Arg w = π then z equals

Options

A.
B.
C.w
D.- w

Solution

Let |z| = |ω| = r ∴ z = reiθ, ω = reiφ where θ + φ = π ∴ = re-iφ
∴ z = rei(π - φ) = reiπ .eiπ = - reiφ = -

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