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Simplifying (5 + -2i)(4 + -6i) = 0 Multiply (5 + -2i) * (4 + -6i) (5(4 + -6i) + -2i * (4 + -6i)) = 0 ((4 * 5 + -6i * 5) + -2i * (4 + -6i)) = 0 ((20 + -30i) + -2i * (4 + -6i)) = 0 (20 + -30i + (4 * -2i + -6i * -2i)) = 0 (20 + -30i + (-8i + 12i2)) = 0 Combine like terms: -30i + -8i = -38i (20 + -38i + 12i2) = 0 Solving 20 + -38i + 12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -19i + 6i2) = 0 Factor a trinomial. 2((2 + -3i)(5 + -2i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 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 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 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 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Solution
i = {0.6666666667, 2.5}
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