What is (-2+(i-1)/n)^3 ?

The solution to (-2+(i-1)/n)^3 is (-8n^3-12n^2+2)/(n^3)+(12n^2+2+12n)/(n^3)i

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simplify (-2+(i-1)/n)^3

simplify

(- 2 + \frac{i - 1}{n})^{3}

\frac{- 8 n ^{3} - 12 n ^{2} + 2}{n ^{3}} + \frac{12 n ^{2} + 2 + 12 n}{n ^{3}} i

Solution steps

(- 2 + \frac{i - 1}{n})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(- 2 + \frac{i - 1}{n})^{3} = (- 2)^{3} + 3 (- 2)^{2} \frac{i - 1}{n} + 3 (- 2) (\frac{i - 1}{n})^{2} + (\frac{i - 1}{n})^{3}

= (- 2)^{3} + 3 (- 2)^{2} \frac{i - 1}{n} + 3 (- 2) (\frac{i - 1}{n})^{2} + (\frac{i - 1}{n})^{3}

Simplify

(- 2)^{3} + 3 (- 2)^{2} \frac{i - 1}{n} + 3 (- 2) (\frac{i - 1}{n})^{2} + (\frac{i - 1}{n})^{3} : \frac{- 8 n ^{3} - 12 n ^{2} + 2}{n ^{3}} + \frac{12 n ^{2} + 2 + 12 n}{n ^{3}} i

= \frac{- 8 n ^{3} - 12 n ^{2} + 2}{n ^{3}} + \frac{12 n ^{2} + 2 + 12 n}{n ^{3}} i

(3 - x + 1)^{2}

lo g_{10} (3) (x - 1)

cos ((2 n + 1) π)

V (0, - 3) F (- 3, - 3)

(D^{2} - D + 3) [x^{3} e^{- 2 x}]

What is (-2+(i-1)/n)^3 ?
The solution to (-2+(i-1)/n)^3 is (-8n^3-12n^2+2)/(n^3)+(12n^2+2+12n)/(n^3)i