simplify (8+i/n)^2

Solution

simplify

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

\frac{64 n ^{2} - 1}{n ^{2}} + \frac{16}{n} i

Solution steps

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

Apply Perfect Square Formula:

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

(8 + \frac{i}{n})^{2} = 8^{2} + 2 \cdot 8 \cdot \frac{i}{n} + (\frac{i}{n})^{2}

= 8^{2} + 2 \cdot 8 \cdot \frac{i}{n} + (\frac{i}{n})^{2}

Simplify

8^{2} + 2 \cdot 8 \cdot \frac{i}{n} + (\frac{i}{n})^{2} : \frac{64 n ^{2} - 1}{n ^{2}} + \frac{16}{n} i

= \frac{64 n ^{2} - 1}{n ^{2}} + \frac{16}{n} i

e^{2 x} (4 e^{3 x} - 3 e^{- 3 x})

4 - x^{2} \cdot 1 + x

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\frac{2 ( - 3 x + 2 )}{3 x ^{3}}

4 x^{2} - x (8 + 9 x^{4} - 5 x)