If z and w are complex numbers such that bar{ | vedclass

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Question

(B) Given $\bar{z} - i \bar{w} = 0$,we have $\bar{z} = i \bar{w}$.Taking the conjugate on both sides,$z = -i w$,which implies $w = \frac{z}{-i} = iz$.

Vedclass · Accepted Answer

$\frac{\pi}{8}$

Vedclass · Answer

(B) Given $\bar{z} - i \bar{w} = 0$,we have $\bar{z} = i \bar{w}$.Taking the conjugate on both sides,$z = -i w$,which implies $w = \frac{z}{-i} = iz$.Now,$\operatorname{Arg}(zw) = \operatorname{Arg}(z(iz)) = \operatorname{Arg}(iz^2) = \frac{3 \pi}{4}$.Using the property $\operatorname{Arg}(z_1 z_2) = \operatorname{Arg}(z_1) + \operatorname{Arg}(z_2)$,we get $\operatorname{Arg}(i) + \operatorname{Arg}(z^2) = \frac{3 \pi}{4}$.Since $\operatorname{Arg}(i) = \frac{\pi}{2}$ and $\operatorname{Arg}(z^2) = 2 \operatorname{Arg}(z)$,we have $\frac{\pi}{2} + 2 \operatorname{Arg}(z) = \frac{3 \pi}{4}$.$2 \operatorname{Arg}(z) = \frac{3 \pi}{4} - \frac{\pi}{2} = \frac{\pi}{4}$.Therefore,$\operatorname{Arg}(z) = \frac{\pi}{8}$.

If $z$ and $w$ are complex numbers such that $\bar{z} - i \bar{w} = 0$ and $\operatorname{Arg}(zw) = \frac{3 \pi}{4}$,then $\operatorname{Arg} z =$

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