Question

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

• A. 244
• B. 224
• C. 245
• D. 265

Answer 1

Answer: (A)

$z^5+(\bar{z}{)}^5=(2+3i{)}^5+(2-3i{)}^5$
$=2\left({}^5{C}_0{2}^5+{}^5{C}_2{2}^3(3i{)}^2+{}^5{C}_4{2}^1(3i{)}^4\right)$
$=2(32+10\times 8(-9)+5\times 2\times 81)=244$