Past exam of the mathematical methods I course of the University of Oxford / 2019 resit / 1 / a

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- Solution a

Solution

Since

(1 - i)^{3} = - 2 - 2 i

, divide and multiply by the complex conjugate of the denominator:

\frac{i}{( 1 - i ) ^{3}} = \frac{i ( - 2 + 2 i )}{8} = - \frac{1}{4} - \frac{1}{4} i .

Multiplication by

- 2 - 2 i

verifies the result directly.

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