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

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

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

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

2 \cdot \frac{2 i}{n} \cdot 1 = 2 \cdot \frac{2 i}{n}

1^{2} = 1

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

Simplify

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

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

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