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Simplifying (6 + -3i)(5 + 4i) = 0 Multiply (6 + -3i) * (5 + 4i) (6(5 + 4i) + -3i * (5 + 4i)) = 0 ((5 * 6 + 4i * 6) + -3i * (5 + 4i)) = 0 ((30 + 24i) + -3i * (5 + 4i)) = 0 (30 + 24i + (5 * -3i + 4i * -3i)) = 0 (30 + 24i + (-15i + -12i2)) = 0 Combine like terms: 24i + -15i = 9i (30 + 9i + -12i2) = 0 Solving 30 + 9i + -12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 3i + -4i2) = 0 Factor a trinomial. 3((2 + -1i)(5 + 4i)) = 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 + 4i)' equal to zero and attempt to solve: Simplifying 5 + 4i = 0 Solving 5 + 4i = 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 + 4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4i = 0 + -5 4i = 0 + -5 Combine like terms: 0 + -5 = -5 4i = -5 Divide each side by '4'. i = -1.25 Simplifying i = -1.25Solution
i = {2, -1.25}
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