Question

Express each of the complex number given in the Exercises $1$ to $10$ in the form $a+ib$.
$i^{-39}$

Answer 1

$i=\sqrt{-1}\Rightarrow i^2=-1$

$i^{-39}$

$=\frac{1}{i^{39}}$

$=\frac{1}{i^{38}\times i^1}$

$=\frac{1}{(-1)\times i^1}$

$=\frac{1}{-i}$

multiply and divide by $-i$, we get,

$=\frac{-i}{-1}$

$=0+1\times i$