Complex NumbersHard

Question

Let z and w be two non-zero complex number such that |z| = |w| and arg (z) + arg π, then z equals

Options

A.w
B.- w
C.
D.

Solution

Since, |z| = |w | and arg (z) = π - arg(w)
Let     w = reiθ, then = re- iθ
∴     z = rei(π-θ) = reiπ . re-iθ
       = - re-iθ = -

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