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

The solution to (2+(2i)/n)^2 is (4n^2-4)/(n^2)+8/n i

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simplify (2+(2i)/n)^2

simplify

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

\frac{4 n ^{2} - 4}{n ^{2}} + \frac{8}{n} i

Solution steps

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

Apply Perfect Square Formula:

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

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

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

2^{2} = 4

2 \cdot 2 \cdot \frac{2 i}{n} = 4 \cdot \frac{2 i}{n}

(\frac{2 i}{n})^{2} = - \frac{4}{n ^{2}}

= 4 + 4 \cdot \frac{2 i}{n} - \frac{4}{n ^{2}}

Simplify

4 + 4 \cdot \frac{2 i}{n} - \frac{4}{n ^{2}} : \frac{4 n ^{2} - 4}{n ^{2}} + \frac{8}{n} i

= \frac{4 n ^{2} - 4}{n ^{2}} + \frac{8}{n} i

(x + 1)^{3}

\frac{1}{( x - 1 ) ( x - 3 )}

(0, - 1) y (1, 1)

cos (x + y) (1 + \frac{d y}{d x})

(b + c) (d - e)