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Simplifying (5 + -6i)(3 + -2i) = 0 Multiply (5 + -6i) * (3 + -2i) (5(3 + -2i) + -6i * (3 + -2i)) = 0 ((3 * 5 + -2i * 5) + -6i * (3 + -2i)) = 0 ((15 + -10i) + -6i * (3 + -2i)) = 0 (15 + -10i + (3 * -6i + -2i * -6i)) = 0 (15 + -10i + (-18i + 12i2)) = 0 Combine like terms: -10i + -18i = -28i (15 + -28i + 12i2) = 0 Solving 15 + -28i + 12i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -6i)(3 + -2i) = 0Subproblem 1
Set the factor '(5 + -6i)' equal to zero and attempt to solve: Simplifying 5 + -6i = 0 Solving 5 + -6i = 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 + -6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6i = 0 + -5 -6i = 0 + -5 Combine like terms: 0 + -5 = -5 -6i = -5 Divide each side by '-6'. i = 0.8333333333 Simplifying i = 0.8333333333Subproblem 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 = {0.8333333333, 1.5}
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