R S Aggarwal Solutions for Exercise 7: EXERCISE 5G

Evaluate $\left(\frac{i^{180}+i^{178}+i^{176}+i^{174}+i^{172}}{i^{170}+i^{168}+i^{166}+i^{164}+i^{162}}\right)$

Express $\left(\frac{3-\sqrt{-16}}{1-\sqrt{-9}}\right)$ in the form $(a+ib)$.

Find the conjugate of $\frac{1}{(3+4i)}$.

If $z=(1-i)$, find $z^{-1}$.

If $z=(\sqrt{5}+3i)$ and $z^{-1} =\frac{\sqrt{5}}{k}+\frac{3}{k}i$, then the value of $2k$ is

If the principal argument of $(-2i)$ is $\frac{m\mathrm{\pi }}{n}$ then $m+n=$

The principal argument of $(1+i\sqrt{3}{)}^2$ is of the form of $\frac{m\mathrm{\pi }}{3}$, then find the value of $m$.

The polar form of $-9$ is $m\left(\mathrm{cos\pi }+i\mathrm{sin\pi }\right)$, then $m=$