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Simplifying (4 + 2i)(5 + -3i) = 0 Multiply (4 + 2i) * (5 + -3i) (4(5 + -3i) + 2i * (5 + -3i)) = 0 ((5 * 4 + -3i * 4) + 2i * (5 + -3i)) = 0 ((20 + -12i) + 2i * (5 + -3i)) = 0 (20 + -12i + (5 * 2i + -3i * 2i)) = 0 (20 + -12i + (10i + -6i2)) = 0 Combine like terms: -12i + 10i = -2i (20 + -2i + -6i2) = 0 Solving 20 + -2i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -1i + -3i2) = 0 Factor a trinomial. 2((5 + -3i)(2 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 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 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667Subproblem 2
Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {1.666666667, -2}
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