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Simplifying (8 + -3i)(5 + -6i) = 0 Multiply (8 + -3i) * (5 + -6i) (8(5 + -6i) + -3i * (5 + -6i)) = 0 ((5 * 8 + -6i * 8) + -3i * (5 + -6i)) = 0 ((40 + -48i) + -3i * (5 + -6i)) = 0 (40 + -48i + (5 * -3i + -6i * -3i)) = 0 (40 + -48i + (-15i + 18i2)) = 0 Combine like terms: -48i + -15i = -63i (40 + -63i + 18i2) = 0 Solving 40 + -63i + 18i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -6i)(8 + -3i) = 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 '(8 + -3i)' equal to zero and attempt to solve: Simplifying 8 + -3i = 0 Solving 8 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3i = 0 + -8 -3i = 0 + -8 Combine like terms: 0 + -8 = -8 -3i = -8 Divide each side by '-3'. i = 2.666666667 Simplifying i = 2.666666667Solution
i = {0.8333333333, 2.666666667}
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