simplify (-1+i/n)^2

Solution

simplify

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

\frac{n ^{2} - 1}{n ^{2}} - \frac{2}{n} i

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

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

= \frac{n ^{2} - 1}{n ^{2}} - \frac{2}{n} i

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