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Question
Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`
Solution
`(-2 - 1/3 i)^3 = (-1)^3 (2 + 1/3i)^3 = - (2 + 1/3i)^3`
= - `[2^3 + 3.2^2 (1/3i) + 3.2 (1/3i)^2 + (1/3i)^3]`
= `- [ 8 + 4i - 2/3 + 1/(27)i^2 i]`
= `-[22/3 + (4 - 1/27)i]`
= `[- 22/3 -107/27i]`
= - `22/3 - 107/27i`
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