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Simplifying (1 + 3i)(5 + -1i) = 0 Multiply (1 + 3i) * (5 + -1i) (1(5 + -1i) + 3i * (5 + -1i)) = 0 ((5 * 1 + -1i * 1) + 3i * (5 + -1i)) = 0 ((5 + -1i) + 3i * (5 + -1i)) = 0 (5 + -1i + (5 * 3i + -1i * 3i)) = 0 (5 + -1i + (15i + -3i2)) = 0 Combine like terms: -1i + 15i = 14i (5 + 14i + -3i2) = 0 Solving 5 + 14i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -1i)(1 + 3i) = 0Subproblem 1
Set the factor '(5 + -1i)' equal to zero and attempt to solve: Simplifying 5 + -1i = 0 Solving 5 + -1i = 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 + -1i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1i = 0 + -5 -1i = 0 + -5 Combine like terms: 0 + -5 = -5 -1i = -5 Divide each side by '-1'. i = 5 Simplifying i = 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 = {5, -0.3333333333}
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