If Z and W are two non-zero complex numbers such that |ZW| = 1 and $\arg (Z) - \arg (W) = \frac{π}{2}$ , then the value of $5 i Z W$ is equal to

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-5

-5i

answer is C.

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Detailed Solution

$a r g z - a r g ω = \frac{π}{2} \Rightarrow - a r g z + a r g ω = - \frac{π}{2} ∴ a r g z ω = - \frac{π}{2}, |z ω| = 1 \Rightarrow |z ω| z ω = |z ω| e^{i a r g z ω} = e^{- i \frac{π}{2}} = - i$
$5 i \bar{Z} ω = 5 i (- i) = 5$

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