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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 = -14i (-12 + -14i + -4i2) = 0 Solving -12 + -14i + -4i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(6 + 7i + 2i2) = 0 Factor a trinomial. -2((2 + i)(3 + 2i)) = 0 Ignore the factor -2.Subproblem 1
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 = -2Subproblem 2
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 = -1.5Solution
i = {-2, -1.5}
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