If z=2+3 i, then [z^5+(z)^5] is equal to :

Question

If $z=2+3 i$, then $$z^{5}+(\bar{z})^{5}$$ is equal to :

Accepted Answer

$z = (2 + 3i)$

$$ \Rightarrow {z^5} = (2 + 3i){\left( {{{(2 + 3i)}^2}} \right)^2}$$

$= (2 + 3i){( - 5 + 12i)^2}$

$= (2 + 3i)( - 119 - 120i)$

$=  - 238 - 240i - 357i + 360$

$= 122 - 597i$

$${\overline z ^5} = 122 + 597i$$

$${z^5} + {\overline z ^5} = 244$$

Solutions · 1