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Simplifying (3 + -2i)(-4 + -6i) = 0 Multiply (3 + -2i) * (-4 + -6i) (3(-4 + -6i) + -2i * (-4 + -6i)) = 0 ((-4 * 3 + -6i * 3) + -2i * (-4 + -6i)) = 0 ((-12 + -18i) + -2i * (-4 + -6i)) = 0 (-12 + -18i + (-4 * -2i + -6i * -2i)) = 0 (-12 + -18i + (8i + 12i2)) = 0 Combine like terms: -18i + 8i = -10i (-12 + -10i + 12i2) = 0 Solving -12 + -10i + 12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -5i + 6i2) = 0 Factor a trinomial. 2((-2 + -3i)(3 + -2i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -3i)' equal to zero and attempt to solve: Simplifying -2 + -3i = 0 Solving -2 + -3i = 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 + -3i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3i = 0 + 2 -3i = 0 + 2 Combine like terms: 0 + 2 = 2 -3i = 2 Divide each side by '-3'. i = -0.6666666667 Simplifying i = -0.6666666667Subproblem 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 = {-0.6666666667, 1.5}
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