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Simplifying (-2 + 4i)(-5 + 6i) = 0 Multiply (-2 + 4i) * (-5 + 6i) (-2(-5 + 6i) + 4i * (-5 + 6i)) = 0 ((-5 * -2 + 6i * -2) + 4i * (-5 + 6i)) = 0 ((10 + -12i) + 4i * (-5 + 6i)) = 0 (10 + -12i + (-5 * 4i + 6i * 4i)) = 0 (10 + -12i + (-20i + 24i2)) = 0 Combine like terms: -12i + -20i = -32i (10 + -32i + 24i2) = 0 Solving 10 + -32i + 24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -16i + 12i2) = 0 Factor a trinomial. 2((1 + -2i)(5 + -6i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 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 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5Subproblem 2
Set the factor '(5 + -6i)' equal to zero and attempt to solve: Simplifying 5 + -6i = 0 Solving 5 + -6i = 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 + -6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6i = 0 + -5 -6i = 0 + -5 Combine like terms: 0 + -5 = -5 -6i = -5 Divide each side by '-6'. i = 0.8333333333 Simplifying i = 0.8333333333Solution
i = {0.5, 0.8333333333}
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