QJEEM22Mae9ce: JEE Main 2022 Mathematics - Class 11 JEEM22Mae9ce Solution: If z = 2 + 3 i , then z 5 + ( z ¯ ) 5 is equal to :

Question

Verified Solution • 2025–26 Session moderate

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

Accepted Answer

$z = (2 + 3 i)$

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

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

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

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

$= 122 - 597 i$

${\overset{―}{z}}^{5} = 122 + 597 i$

$z^{5} + {\overset{―}{z}}^{5} = 244$

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