Solve \left(\frac{i}{1-i}\right)^3 - ScanMath

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Question

Simplify the expression

\frac{1}{4} + \frac{1}{4} i

Evaluate

(\frac{i}{1 - i})^{3}

Divide the terms

More Steps

(- \frac{1}{2} + \frac{1}{2} i)^{3}

Use (a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} to expand the expression

(- \frac{1}{2})^{3} + 3 (- \frac{1}{2})^{2} \times \frac{1}{2} i + 3 (- \frac{1}{2}) (\frac{1}{2} i)^{2} + (\frac{1}{2} i)^{3}

Evaluate

More Steps

- \frac{1}{8} + 3 (- \frac{1}{2})^{2} \times \frac{1}{2} i + 3 (- \frac{1}{2}) (\frac{1}{2} i)^{2} + (\frac{1}{2} i)^{3}

Evaluate

More Steps

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

Evaluate

More Steps

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

Evaluate

More Steps

- \frac{1}{8} + \frac{3}{8} i + \frac{3}{8} - \frac{1}{8} i

Solution

\frac{1}{4} + \frac{1}{4} i

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