Question

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

• A. 244
• B. 224
• C. 245
• D. 265

Answer 1

Answer: (A)

244

Answer 2

$z = (2 + 3i)$
$⇒$ $z^5 = (2 + 3i)((2 + 3i)^2)^2$
$= (2 + 3i) (-5 + 12i)^2$
$= (2 + 3i)(-119 – 120i)$
$= – 238 – 240i – 357i \+ 360$
$= 122 – 597i$
$\overline{z}^5 = 122 + 597i$
$z^5 + \overline{z}^5 = 244$
So, the correct option is (A): 244