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