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Write in standard form: ( 1 - 3i ) the whole raised to -3

$\frac{1}{{(1 - 3 i)}^{3}} = \frac{1}{(1 - 3 i) (1 + 3 i + 9 i^{2})} = \frac{1}{(1 - 3 i) (1 + 3 i - 9)} = \frac{1}{(1 - 3 i) (3 i - 8)} = \frac{1}{3 i - 8 - 9 i^{2} + 24 i} = \frac{1}{3 i - 8 + 9 + 24 i} = \frac{1}{1 + 27 i} = \frac{1 - 27 i}{(1 + 27 i) (1 - 27 i)} = \frac{1 - 27 i}{1^{2} - {(27 i)}^{2}} = \frac{1 - 27 i}{1 + 729} = \frac{1 - 27 i}{730} = \frac{1}{730} - \frac{27}{730} i$

-2

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