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Simplifying (5 + 6i)(2 + -3i) = 0 Multiply (5 + 6i) * (2 + -3i) (5(2 + -3i) + 6i * (2 + -3i)) = 0 ((2 * 5 + -3i * 5) + 6i * (2 + -3i)) = 0 ((10 + -15i) + 6i * (2 + -3i)) = 0 (10 + -15i + (2 * 6i + -3i * 6i)) = 0 (10 + -15i + (12i + -18i2)) = 0 Combine like terms: -15i + 12i = -3i (10 + -3i + -18i2) = 0 Solving 10 + -3i + -18i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -3i)(5 + 6i) = 0Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 2
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 = -0.8333333333Solution
i = {0.6666666667, -0.8333333333}
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