Question

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of factoring polynomials and identities for imaginary numbers.

x^3-27i

Answer 1

i^3=-i
therefor -27i=(3i)^3
so we can get a sum of 2 perfect cubes
a^3+b^3=(a+b)(a^2-ab+b^2)

so
remember that i²=-1
x^3+(3i)^3=(x+3i)(x²-3xi-1)