Question

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

• A. 0 + 0i
• B. 1 + 0i
• C. 0 + i
• D. 1 + 2 i

Answer 1

Answer: (A)

0 + 0i

Answer 2

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