What is (-1+(2i)/n)^2 ?

The solution to (-1+(2i)/n)^2 is (n^2-4)/(n^2)-4/n i

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simplify (-1+(2i)/n)^2

simplify

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

\frac{n ^{2} - 4}{n ^{2}} - \frac{4}{n} i

Solution steps

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

Apply Perfect Square Formula:

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

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

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

(- 1)^{2} = 1

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

(\frac{2 i}{n})^{2} = - \frac{4}{n ^{2}}

= 1 - 2 \cdot \frac{2 i}{n} - \frac{4}{n ^{2}}

Simplify

1 - 2 \cdot \frac{2 i}{n} - \frac{4}{n ^{2}} : \frac{n ^{2} - 4}{n ^{2}} - \frac{4}{n} i

= \frac{n ^{2} - 4}{n ^{2}} - \frac{4}{n} i

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