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}

Simplify

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

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

x (\frac{( 3 x - 10 ) ^{3}}{100} + 10)

m sin (\frac{π}{6} (k + 1)) + n cos (\frac{π}{6} (k + 1))

(36 + a^{2} + 64 + b^{2})^{2}

(x + 3 - 5) (x + 3 + 5)