simplify (i/n+1)^2

Solution

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

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

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

1^{2} = 1

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

Simplify

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

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

- \frac{3 ( 7 - 2 5 )}{29}

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