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Simplifying (5 + 3i)(6 + -3i) = 0 Multiply (5 + 3i) * (6 + -3i) (5(6 + -3i) + 3i * (6 + -3i)) = 0 ((6 * 5 + -3i * 5) + 3i * (6 + -3i)) = 0 ((30 + -15i) + 3i * (6 + -3i)) = 0 (30 + -15i + (6 * 3i + -3i * 3i)) = 0 (30 + -15i + (18i + -9i2)) = 0 Combine like terms: -15i + 18i = 3i (30 + 3i + -9i2) = 0 Solving 30 + 3i + -9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + i + -3i2) = 0 Factor a trinomial. 3((2 + -1i)(5 + 3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
Set the factor '(5 + 3i)' equal to zero and attempt to solve: Simplifying 5 + 3i = 0 Solving 5 + 3i = 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 + 3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3i = 0 + -5 3i = 0 + -5 Combine like terms: 0 + -5 = -5 3i = -5 Divide each side by '3'. i = -1.666666667 Simplifying i = -1.666666667Solution
i = {2, -1.666666667}
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