Question

Express in the form of $a+ib$ :

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

Answer 1

We know,

$(a+b{)}^3=a^3+3a^{2}b+3a{b}^2+b^3$

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

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

$=\frac{1}{27}+27i^3+3i(\frac{1}{3}+3i)$

$=\frac{1}{27}+27i^3+i+9i^2$

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

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