Question

Complex Roots

What are the roots of the equation x^2 + 2x + 65 = 0 in simplest a + bi form?

Answer 1

`x=-1\pm8i`

Explanation:

Complete the square of LHS and solve for x

`x^2+2x+65=0\\x^2+2x+1=-64\\(x+1)^2=-64\\x+1=\pm8i\\x=-1\pm8i`