Find the set of values of $\alpha $ for which the expression \(\frac{2-\mathbf{i}\sin \,2\alpha }{

Question

Find the set of values of $\alpha $ for which the expression $\frac{2-\mathbf{i}\sin \,2\alpha }{1+2\,\mathbf{i}\,\sin \,2\alpha }$ is purely real.[3] If $z$ and $w$ are different non-zero complex numbers and $\left| w \right|=1$, find $\left| \frac{3\left( w-z \right)}{1-{{z}^{*}}w} \right|$.[4]

Accepted Answer

$\text{(a)}\ \alpha=\dfrac{k\pi}{2},\ k\in\mathbb{Z}$ $\text{(b)}\ 3$

2023 DHS P1 Q4

2023 DHS P1 Q4

Video Solution:

Solution:

Solution locked