simplify (x+i)^3

Solution

simplify

(x + i)^{3}

(x^{3} - 3 x) + (3 x^{2} - 1) i

Solution steps

(x + i)^{3}

Apply Perfect Cube Formula:

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

(x + i)^{3} = x^{3} + 3 x^{2} i + 3 x i^{2} + i^{3}

= x^{3} + 3 x^{2} i + 3 x i^{2} + i^{3}

3 x i^{2} = - 3 x

i^{3} = - i

= x^{3} + 3 x^{2} i - 3 x - i

Rewrite in standard complex form:

(x^{3} - 3 x) + (3 x^{2} - 1) i

= (x^{3} - 3 x) + (3 x^{2} - 1) i

(y + 1)^{2}

(3 y + 5 i)^{2}

tan (\frac{x}{2}) + (1 - cos (x)) cot (x)

\frac{2 x + 1}{( x - 1 ) ^{2}}

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