First slide

Algebra of complex numbers

Question

Let $z, w$ be two complex numbers such that $\bar{z} + i \bar{w} = 0$ and $a r g (z w) = π,$ then $a r g z$ equal

Moderate

A

$\frac{3 π}{4}$
B

$\frac{π}{2}$
C

$\frac{π}{4}$
D

$\frac{5 π}{4}$

Solution

$\bar{z} + i \bar{w} = 0 \Rightarrow z - i w = 0$
Now, $a r g (z w) = π \Rightarrow a r g (\frac{z^{2}}{i}) = π$
$\Rightarrow 2 a r g (z) - a r g (i) = π$
$\Rightarrow 2 a r g (z) = π + \frac{π}{2} = \frac{3 π}{2} \Rightarrow a r g (z) = \frac{3 π}{4}$

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