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

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

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expand (1+1/n i)^2

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

Rewrite in standard complex form:

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

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

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