Question

\\ {z}^{5} = " alt="z = 3 + i \\ {z}^{5} = " align="absmiddle" class="latex-formula">??
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Answer 1

Answer:

$z^{5}$ =  - 12 + 316 i

Step-by-step explanation:

Given that -

z = 3 + i

$z^{2}$ = $( 3 + i )^{2}$

$z^{2}$ = 9 + $i^{2}$ + 6 i

$z^{2}$ = 9 - 1 + 6 i

$z^{2}$ = 8 + 6 i

$z^{3}$ = $z^{2}$ × z

$z^{3}$ = ( 8 + 6 i ) × ( 3 + i )

$z^{3}$ = 24 + 8 i + 18 i + 6 i²

$z^{3}$ = 24 + 26 i - 6

$z^{3}$ = 18 + 26 i

$z^{5}$ = $z^{2}$ × $z^{3}$

$z^{5}$ = ( 8 + 6 i ) × ( 18 + 26 i )

$z^{5}$ = 144 + 208 i + 108 i + 156 i²

$z^{5}$ = 144 + 316 i -156

$z^{5}$ =  - 12 + 316 i