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Simplifying (3 + -3i)(4 + 2i) = 0 Multiply (3 + -3i) * (4 + 2i) (3(4 + 2i) + -3i * (4 + 2i)) = 0 ((4 * 3 + 2i * 3) + -3i * (4 + 2i)) = 0 ((12 + 6i) + -3i * (4 + 2i)) = 0 (12 + 6i + (4 * -3i + 2i * -3i)) = 0 (12 + 6i + (-12i + -6i2)) = 0 Combine like terms: 6i + -12i = -6i (12 + -6i + -6i2) = 0 Solving 12 + -6i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(2 + -1i + -1i2) = 0 Factor a trinomial. 6((1 + -1i)(2 + i)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 2
Set the factor '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {1, -2}
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