Question

Express the given complex number in the form $a + ib: i^{9} + i^{19}$

Answer 1

$i^{9} + i^{19}=i^{4×2+1}+i^{4×4+1}$

$=(i^{4})^{2} ×i +(i^{4})^{4} × i^{3}$

$=1×i +1×(-i)$

$=0$