<img src="https://tex.z-dn.net/?f=z%20%3D%203%20%2B%20i%20%5C%5C%20%7Bz%7D%5E%7B5%7D%20%3D%20" id="TexFormula1" title="z = 3 + i

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alexandr1967 [171]

3 years ago

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

Mathematics

1 answer:

jarptica [38.1K]3 years ago

6 0

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

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