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Simplifying (6 + -3i)(-4 + 6i) = 0 Multiply (6 + -3i) * (-4 + 6i) (6(-4 + 6i) + -3i * (-4 + 6i)) = 0 ((-4 * 6 + 6i * 6) + -3i * (-4 + 6i)) = 0 ((-24 + 36i) + -3i * (-4 + 6i)) = 0 (-24 + 36i + (-4 * -3i + 6i * -3i)) = 0 (-24 + 36i + (12i + -18i2)) = 0 Combine like terms: 36i + 12i = 48i (-24 + 48i + -18i2) = 0 Solving -24 + 48i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + 8i + -3i2) = 0 Factor a trinomial. 6((-2 + i)(2 + -3i)) = 0 Ignore the factor 6.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 '(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 = 0.6666666667Solution
i = {2, 0.6666666667}
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