Question

Express $(\frac{1}{3}+3i{)}^3$ in the form $a+ib$.

• A. $\frac{343}{34}+23i$
• B. $-\frac{343}{34}-23i$
• C. $\frac{242}{27}+26i$
• D. $-\frac{242}{27}-26i$

Answer 1

Answer: (D)

$-\frac{242}{27}-26i$

$(\frac{1}{3}+3i{)}^3$

$=(\frac{1}{3}{)}^3+(3i{)}^3+3\left(\frac{1}{3}\right)\left(3i\right)(\frac{1}{3}+3i)$

$=\frac{1}{27}-27i+i+9i^2$

$=(\frac{1}{27}-9)-26i$

$=-\frac{242}{27}-26i$