Question

Convert the following into a + ib form.
(1/3 + 3i )^3

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Answer 1

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

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

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

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

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