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Simplifying (5 + 2i)(1 + 3i) = 0 Multiply (5 + 2i) * (1 + 3i) (5(1 + 3i) + 2i * (1 + 3i)) = 0 ((1 * 5 + 3i * 5) + 2i * (1 + 3i)) = 0 ((5 + 15i) + 2i * (1 + 3i)) = 0 (5 + 15i + (1 * 2i + 3i * 2i)) = 0 (5 + 15i + (2i + 6i2)) = 0 Combine like terms: 15i + 2i = 17i (5 + 17i + 6i2) = 0 Solving 5 + 17i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + 2i)(1 + 3i) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve: Simplifying 1 + 3i = 0 Solving 1 + 3i = 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 + 3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3i = 0 + -1 3i = 0 + -1 Combine like terms: 0 + -1 = -1 3i = -1 Divide each side by '3'. i = -0.3333333333 Simplifying i = -0.3333333333Solution
i = {-2.5, -0.3333333333}
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