Question:
Express the given complex number in the form $a+i b: i^{9}+i^{19}$
Solution:
$i^{9}+i^{19}=i^{4 \times 2+1}+i^{4 \times 4+3}$
$=\left(i^{4}\right)^{2} \cdot i+\left(i^{4}\right)^{4} \cdot i^{3}$
$=1 \times i+1 \times(-i) \quad\left[i^{4}=1, i^{3}=-i\right]$
$=i+(-i)$
$=0$