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Simplifying (4 + 4i)(-2 + 5i) = 0 Multiply (4 + 4i) * (-2 + 5i) (4(-2 + 5i) + 4i * (-2 + 5i)) = 0 ((-2 * 4 + 5i * 4) + 4i * (-2 + 5i)) = 0 ((-8 + 20i) + 4i * (-2 + 5i)) = 0 (-8 + 20i + (-2 * 4i + 5i * 4i)) = 0 (-8 + 20i + (-8i + 20i2)) = 0 Combine like terms: 20i + -8i = 12i (-8 + 12i + 20i2) = 0 Solving -8 + 12i + 20i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 3i + 5i2) = 0 Factor a trinomial. 4((-1 + -1i)(2 + -5i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -1i)' equal to zero and attempt to solve: Simplifying -1 + -1i = 0 Solving -1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1i = 0 + 1 -1i = 0 + 1 Combine like terms: 0 + 1 = 1 -1i = 1 Divide each side by '-1'. i = -1 Simplifying i = -1Subproblem 2
Set the factor '(2 + -5i)' equal to zero and attempt to solve: Simplifying 2 + -5i = 0 Solving 2 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5i = 0 + -2 -5i = 0 + -2 Combine like terms: 0 + -2 = -2 -5i = -2 Divide each side by '-5'. i = 0.4 Simplifying i = 0.4Solution
i = {-1, 0.4}
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