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Simplifying (1 + 2i)(5 + -3i) = 0 Multiply (1 + 2i) * (5 + -3i) (1(5 + -3i) + 2i * (5 + -3i)) = 0 ((5 * 1 + -3i * 1) + 2i * (5 + -3i)) = 0 ((5 + -3i) + 2i * (5 + -3i)) = 0 (5 + -3i + (5 * 2i + -3i * 2i)) = 0 (5 + -3i + (10i + -6i2)) = 0 Combine like terms: -3i + 10i = 7i (5 + 7i + -6i2) = 0 Solving 5 + 7i + -6i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -3i)(1 + 2i) = 0Subproblem 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 '(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 = {1.666666667, -0.5}
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