What is expand (1+(3i)/n)^2 ?

The solution to expand (1+(3i)/n)^2 is (n^2-9)/(n^2)+6/n i

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expand (1+(3i)/n)^2

expand

(1 + \frac{3 i}{n})^{2}

\frac{n ^{2} - 9}{n ^{2}} + \frac{6}{n} i

Solution steps

(1 + \frac{3 i}{n})^{2}

Apply Perfect Square Formula:

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

(1 + \frac{3 i}{n})^{2} = 1^{2} + 2 \cdot 1 \cdot \frac{3 i}{n} + (\frac{3 i}{n})^{2}

= 1^{2} + 2 \cdot 1 \cdot \frac{3 i}{n} + (\frac{3 i}{n})^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot \frac{3 i}{n} + (\frac{3 i}{n})^{2} : \frac{n ^{2} - 9}{n ^{2}} + \frac{6}{n} i

= \frac{n ^{2} - 9}{n ^{2}} + \frac{6}{n} i

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What is expand (1+(3i)/n)^2 ?
The solution to expand (1+(3i)/n)^2 is (n^2-9)/(n^2)+6/n i