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

The solution to (4+(2i)/n)^2 is (16n^2-4}{n^2}+\frac{16)/n i

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

4^{2} = 16

2 \cdot 4 \cdot \frac{2 i}{n} = 8 \cdot \frac{2 i}{n}

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

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

Simplify

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

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

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What is (4+(2i)/n)^2 ?
The solution to (4+(2i)/n)^2 is (16n^2-4}{n^2}+\frac{16)/n i