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Simplifying (4 + 2i)(3 + -2i) = 0 Multiply (4 + 2i) * (3 + -2i) (4(3 + -2i) + 2i * (3 + -2i)) = 0 ((3 * 4 + -2i * 4) + 2i * (3 + -2i)) = 0 ((12 + -8i) + 2i * (3 + -2i)) = 0 (12 + -8i + (3 * 2i + -2i * 2i)) = 0 (12 + -8i + (6i + -4i2)) = 0 Combine like terms: -8i + 6i = -2i (12 + -2i + -4i2) = 0 Solving 12 + -2i + -4i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1i + -2i2) = 0 Factor a trinomial. 2((3 + -2i)(2 + i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Subproblem 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 = {1.5, -2}
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