What is (1+(4i)/n)^2 ?

The solution to (1+(4i)/n)^2 is (n^2-16)/(n^2)+8/n i

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simplify (1+(4i)/n)^2

simplify

(1 + \frac{4 i}{n})^{2}

\frac{n ^{2} - 16}{n ^{2}} + \frac{8}{n} i

Solution steps

(1 + \frac{4 i}{n})^{2}

Apply Perfect Square Formula:

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

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

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

1^{2} = 1

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

(\frac{4 i}{n})^{2} = - \frac{16}{n ^{2}}

= 1 + 2 \cdot \frac{4 i}{n} - \frac{16}{n ^{2}}

Simplify

1 + 2 \cdot \frac{4 i}{n} - \frac{16}{n ^{2}} : \frac{n ^{2} - 16}{n ^{2}} + \frac{8}{n} i

= \frac{n ^{2} - 16}{n ^{2}} + \frac{8}{n} i

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