The complex number $u$ is given by $u=\cos heta +\mathrm{i}\sin heta $, where $0Express $u-1$ in

Question

The complex number $u$ is given by $u=\cos 	heta +\mathrm{i}\sin 	heta $, where $0Express $u-1$ in terms of $\sin \frac{	heta }{2}$ and $\cos \frac{	heta }{2}$. Hence, find $\left| u-1 ight|$ and show $\arg \left( u-1 ight)=\frac{\pi }{2}+\frac{	heta }{2}$. [4] Given that $v=-\sqrt{3}+\mathrm{i}$ and ${{\left( v*u ight)}^{8}}$ is real and negative, find the smallest value of $	heta $ in terms of $\pi$. [2]

Accepted Answer

$\theta = \frac{5}{24}\pi$

2018 AJC P1 Q8 (b)

2018 AJC P1 Q8 (b)

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