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Popular >

simplify (3+i/n)^2

Solution

simplify

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

Solution

\frac{9 n ^{2} - 1}{n ^{2}} + \frac{6}{n} i

Solution steps

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

Apply Perfect Square Formula:

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

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

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

3^{2} = 9

2 \cdot 3 \cdot \frac{i}{n} = 6 \cdot \frac{i}{n}

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

= 9 + 6 \cdot \frac{i}{n} - \frac{1}{n ^{2}}

Simplify

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

= \frac{9 n ^{2} - 1}{n ^{2}} + \frac{6}{n} i

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Frequently Asked Questions (FAQ)

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