If $z_{1}$ and $z_{2}$ are conjugate to each other, then find agr (- $z_{1}$ $z_{2}$ ).

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Solution

let $a r g (z_{1}) = θ ⟹ a r g (z_{2}) = - θ$ $∵ z_{1} z_{2}$ are conjugate
$⟹ a r g (- z_{1} = θ - π)$
$a r g (a b) = a r g (a) + a r g (b) ⟹ a r g (- z_{1} z_{2}) = θ - π - θ = - π$

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