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Question
Express the given complex number in the form a + ib: `(1/3 + 3i)^3`
Solution
`(1/3 + 3i)^3 = (1/3)^3 + 3 (1/3)^2 (3i) + 3(1/3) (3i)^2 + (3i)^3`
= `1/27 + 27i^3 + 9i^2`
= `1/27 + 27 (-i) + i + 9 (-1)`
= `1/27 - 9 + i (1 - 27)`
= `(1 - 243)/27 + i (-26)`
= `(- 242)/27 - 26i`
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