Question

solve for the x over the complex numbers.
x² + 4x + 13 = 0
select both solutions.
□ -2 + 3i
□ -1 - 2i
□ -1 + 2i
□ -2 - 3i

Explanation:

Step1: Use quadratic formula

For \(ax^2 + bx + c = 0\), \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 1\), \(b = 4\), \(c = 13\).

Step2: Calculate discriminant

\(b^2 - 4ac = 4^2 - 4\times1\times13 = 16 - 52 = -36\).

Step3: Simplify square root

\(\sqrt{-36}=\sqrt{36}\times\sqrt{-1}=6i\).

Step4: Solve for x

\(x=\frac{-4\pm6i}{2\times1}=-2\pm3i\).

Answer:

-2 + 3i, -2 - 3i