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Simplifying (4 + 6i)(-3 + 3i) = 0 Multiply (4 + 6i) * (-3 + 3i) (4(-3 + 3i) + 6i * (-3 + 3i)) = 0 ((-3 * 4 + 3i * 4) + 6i * (-3 + 3i)) = 0 ((-12 + 12i) + 6i * (-3 + 3i)) = 0 (-12 + 12i + (-3 * 6i + 3i * 6i)) = 0 (-12 + 12i + (-18i + 18i2)) = 0 Combine like terms: 12i + -18i = -6i (-12 + -6i + 18i2) = 0 Solving -12 + -6i + 18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + -1i + 3i2) = 0 Factor a trinomial. 6((-2 + -3i)(1 + -1i)) = 0 Ignore the factor 6.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 '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Solution
i = {-0.6666666667, 1}
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