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Simplifying (5 + -6i)(-2 + 4i) = 0 Multiply (5 + -6i) * (-2 + 4i) (5(-2 + 4i) + -6i * (-2 + 4i)) = 0 ((-2 * 5 + 4i * 5) + -6i * (-2 + 4i)) = 0 ((-10 + 20i) + -6i * (-2 + 4i)) = 0 (-10 + 20i + (-2 * -6i + 4i * -6i)) = 0 (-10 + 20i + (12i + -24i2)) = 0 Combine like terms: 20i + 12i = 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((-5 + 6i)(1 + -2i)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.8333333333Subproblem 2
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 = 0.5Solution
i = {0.8333333333, 0.5}
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