Q. If $z = i^{9} + i^{19}$ , then $z$ is equal to

2102 184 KEAMKEAM 2017Complex Numbers and Quadratic Equations Report Error

A

0 + 0i

40%

B

1 + 0i

30%

C

0 + i

0%

D

1 + 2 i

30%

E

1 + 3i

30%

Solution:

We have
$z = i^{9} + i^{19}$
$= (i^{4})^{2} \cdot i + (i^{4})^{4} \cdot i^{3}$
$= i + i^{3} [∵ i^{4} = 1]$
$= i - i [∵ i^{3} = - i]$
$= 0$
$= 0 + 0 i$