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Simplifying (2 + -6i)(-4 + 3i) = 0 Multiply (2 + -6i) * (-4 + 3i) (2(-4 + 3i) + -6i * (-4 + 3i)) = 0 ((-4 * 2 + 3i * 2) + -6i * (-4 + 3i)) = 0 ((-8 + 6i) + -6i * (-4 + 3i)) = 0 (-8 + 6i + (-4 * -6i + 3i * -6i)) = 0 (-8 + 6i + (24i + -18i2)) = 0 Combine like terms: 6i + 24i = 30i (-8 + 30i + -18i2) = 0 Solving -8 + 30i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 15i + -9i2) = 0 Factor a trinomial. 2((-4 + 3i)(1 + -3i)) = 0 Ignore the factor 2.Subproblem 1
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 = 1.333333333Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {1.333333333, 0.3333333333}
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