If z and ω are non-zero complex numbers such that |z|=|ω| and arg z+arg⁡ω=π then z=

If z and $ω$ are non-zero complex numbers such that $| z | = | ω |$ and $\arg z + \arg ω = π$ then $z =$

A
$ω$
B
$- ω$
C
$ω$
D
$- ω$

Solution:

$\begin{array}{l} : z = r e^{i θ}, ω = r e^{i φ} \\ θ + φ = π ∴ z = r e^{i (π - φ)} = r e^{i π} e^{- i φ} \\ = - r e^{- i φ} = - \bar{ω} \end{array}$

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