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

KEAMKEAM 2017Complex Numbers and Quadratic Equations

Solution:

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 $