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Simplifying (3 + 2i)(1 + -5i) = 0 Multiply (3 + 2i) * (1 + -5i) (3(1 + -5i) + 2i * (1 + -5i)) = 0 ((1 * 3 + -5i * 3) + 2i * (1 + -5i)) = 0 ((3 + -15i) + 2i * (1 + -5i)) = 0 (3 + -15i + (1 * 2i + -5i * 2i)) = 0 (3 + -15i + (2i + -10i2)) = 0 Combine like terms: -15i + 2i = -13i (3 + -13i + -10i2) = 0 Solving 3 + -13i + -10i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -5i)(3 + 2i) = 0Subproblem 1
Set the factor '(1 + -5i)' equal to zero and attempt to solve: Simplifying 1 + -5i = 0 Solving 1 + -5i = 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 + -5i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5i = 0 + -1 -5i = 0 + -1 Combine like terms: 0 + -1 = -1 -5i = -1 Divide each side by '-5'. i = 0.2 Simplifying i = 0.2Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {0.2, -1.5}
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