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alexandr1967 [171]
3 years ago
11

\\ {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

<em>z^{2} = ( 3 + i )^{2}</em>

<em>z^{2} = 9 + i^{2} + 6 i</em>

<em>z^{2} = 9 - 1 + 6 i</em>

z^{2} = 8 + 6 i

<em>z^{3} = z^{2} × z</em>

<em>z^{3} = ( 8 + 6 i ) × ( 3 + i )</em>

<em>z^{3} = 24 + 8 i + 18 i + 6 i²</em>

<em>z^{3} = 24 + 26 i - 6</em>

z^{3} = 18 + 26 i

z^{5} = z^{2} × z^{3}

<em>z^{5} = ( 8 + 6 i ) × ( 18 + 26 i )</em>

<em>z^{5} = 144 + 208 i + 108 i + 156 i²</em>

<em>z^{5} = 144 + 316 i -156</em>

z^{5} =  - 12 + 316 i

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