R D Sharma Solutions for Chapter: Complex Numbers, Exercise 1: EXERCISE 13.1

Evaluate the following:

$i^{457}$

Evaluate $i^{528}$.

 Evaluate $\frac{1}{i^{ 58}}$.

Evaluate $i^{37}+\frac{1}{i^{ 67}}$.

Evaluate ${\left( i^{41}+\frac{1}{i^{257}}\right)}^9$.

Find the value of the expression $\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}$.

Find the value of $1+i^2+i^4+i^6+i^8+\dots +i^{20}$

If the value $(1+i{)}^6+(1-i{)}^3$ is $a+ib$, then find the value of $a+b$.