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Simplifying (7 + -3i)(8 + -6i) = 0 Multiply (7 + -3i) * (8 + -6i) (7(8 + -6i) + -3i * (8 + -6i)) = 0 ((8 * 7 + -6i * 7) + -3i * (8 + -6i)) = 0 ((56 + -42i) + -3i * (8 + -6i)) = 0 (56 + -42i + (8 * -3i + -6i * -3i)) = 0 (56 + -42i + (-24i + 18i2)) = 0 Combine like terms: -42i + -24i = -66i (56 + -66i + 18i2) = 0 Solving 56 + -66i + 18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -33i + 9i2) = 0 Factor a trinomial. 2((4 + -3i)(7 + -3i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Subproblem 2
Set the factor '(7 + -3i)' equal to zero and attempt to solve: Simplifying 7 + -3i = 0 Solving 7 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3i = 0 + -7 -3i = 0 + -7 Combine like terms: 0 + -7 = -7 -3i = -7 Divide each side by '-3'. i = 2.333333333 Simplifying i = 2.333333333Solution
i = {1.333333333, 2.333333333}
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