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Simplifying (-6 + 2i)(-5 + -4i) = 0 Multiply (-6 + 2i) * (-5 + -4i) (-6(-5 + -4i) + 2i * (-5 + -4i)) = 0 ((-5 * -6 + -4i * -6) + 2i * (-5 + -4i)) = 0 ((30 + 24i) + 2i * (-5 + -4i)) = 0 (30 + 24i + (-5 * 2i + -4i * 2i)) = 0 (30 + 24i + (-10i + -8i2)) = 0 Combine like terms: 24i + -10i = 14i (30 + 14i + -8i2) = 0 Solving 30 + 14i + -8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 7i + -4i2) = 0 Factor a trinomial. 2((3 + -1i)(5 + 4i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 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 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Subproblem 2
Set the factor '(5 + 4i)' equal to zero and attempt to solve: Simplifying 5 + 4i = 0 Solving 5 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4i = 0 + -5 4i = 0 + -5 Combine like terms: 0 + -5 = -5 4i = -5 Divide each side by '4'. i = -1.25 Simplifying i = -1.25Solution
i = {3, -1.25}
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