Question
Write in $(\text{i}^{25})^3$ polar form.
Let
$\theta$ be the argument of z and a be the acute angle given by $\tan \alpha=\frac{|\text{Im}\text{(z)|}}{|\text{Re}\text{(z)}|}$ Then, $\tan\alpha=\frac{1}{0}=\infty$ $\Rightarrow \alpha =\frac{\pi}{2}$ Clearly, z lies in fourth quadrant. so $\text{arg(z)}=-\alpha =-\frac{\pi}{2}$ $\therefore$ the polar from of z is $\text{|z|}(\cos\theta+\text{i }\sin\theta)=\cos(-\frac{\pi}{2})+\text{i }\sin(-\frac{\pi}{2})$ Thus, the polar from of $(\text{i}^{25})^3$ is $\cos(\frac{\pi}{2})-\text{i }\sin(\frac{\pi}{2})$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Find the 7th term from the end in the expansion of $\Big(2\text{x}^2-\frac{3}{2\text{x}}\Big)^8$