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Simplifying (3 + -4i)(5 + -6i) = 0 Multiply (3 + -4i) * (5 + -6i) (3(5 + -6i) + -4i * (5 + -6i)) = 0 ((5 * 3 + -6i * 3) + -4i * (5 + -6i)) = 0 ((15 + -18i) + -4i * (5 + -6i)) = 0 (15 + -18i + (5 * -4i + -6i * -4i)) = 0 (15 + -18i + (-20i + 24i2)) = 0 Combine like terms: -18i + -20i = -38i (15 + -38i + 24i2) = 0 Solving 15 + -38i + 24i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -4i)(5 + -6i) = 0Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 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 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75Subproblem 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 = {0.75, 0.8333333333}
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