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Simplifying (6 + 2i)(-4 + -3i) = 0 Multiply (6 + 2i) * (-4 + -3i) (6(-4 + -3i) + 2i * (-4 + -3i)) = 0 ((-4 * 6 + -3i * 6) + 2i * (-4 + -3i)) = 0 ((-24 + -18i) + 2i * (-4 + -3i)) = 0 (-24 + -18i + (-4 * 2i + -3i * 2i)) = 0 (-24 + -18i + (-8i + -6i2)) = 0 Combine like terms: -18i + -8i = -26i (-24 + -26i + -6i2) = 0 Solving -24 + -26i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-2'. -2(12 + 13i + 3i2) = 0 Factor a trinomial. -2((3 + i)(4 + 3i)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Subproblem 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 = {-3, -1.333333333}
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