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Simplifying (6 + -4i)(-4 + -5i) = 0 Multiply (6 + -4i) * (-4 + -5i) (6(-4 + -5i) + -4i * (-4 + -5i)) = 0 ((-4 * 6 + -5i * 6) + -4i * (-4 + -5i)) = 0 ((-24 + -30i) + -4i * (-4 + -5i)) = 0 (-24 + -30i + (-4 * -4i + -5i * -4i)) = 0 (-24 + -30i + (16i + 20i2)) = 0 Combine like terms: -30i + 16i = -14i (-24 + -14i + 20i2) = 0 Solving -24 + -14i + 20i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -7i + 10i2) = 0 Factor a trinomial. 2((-4 + -5i)(3 + -2i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -5i)' equal to zero and attempt to solve: Simplifying -4 + -5i = 0 Solving -4 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5i = 0 + 4 -5i = 0 + 4 Combine like terms: 0 + 4 = 4 -5i = 4 Divide each side by '-5'. i = -0.8 Simplifying i = -0.8Subproblem 2
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {-0.8, 1.5}
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