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Simplifying (4 + 3i)(6 + -3i) = 0 Multiply (4 + 3i) * (6 + -3i) (4(6 + -3i) + 3i * (6 + -3i)) = 0 ((6 * 4 + -3i * 4) + 3i * (6 + -3i)) = 0 ((24 + -12i) + 3i * (6 + -3i)) = 0 (24 + -12i + (6 * 3i + -3i * 3i)) = 0 (24 + -12i + (18i + -9i2)) = 0 Combine like terms: -12i + 18i = 6i (24 + 6i + -9i2) = 0 Solving 24 + 6i + -9i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 2i + -3i2) = 0 Factor a trinomial. 3((2 + -1i)(4 + 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 '(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 = -1.333333333Solution
i = {2, -1.333333333}
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