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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. (1 + -3i)(5 + -2i) = 0Subproblem 1
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 = 0.3333333333Subproblem 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 = {0.3333333333, 2.5}
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