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Simplifying (-1 + 3i)(4 + -6i) = 0 Multiply (-1 + 3i) * (4 + -6i) (-1(4 + -6i) + 3i * (4 + -6i)) = 0 ((4 * -1 + -6i * -1) + 3i * (4 + -6i)) = 0 ((-4 + 6i) + 3i * (4 + -6i)) = 0 (-4 + 6i + (4 * 3i + -6i * 3i)) = 0 (-4 + 6i + (12i + -18i2)) = 0 Combine like terms: 6i + 12i = 18i (-4 + 18i + -18i2) = 0 Solving -4 + 18i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 9i + -9i2) = 0 Factor a trinomial. 2((-2 + 3i)(1 + -3i)) = 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 '(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 = {0.6666666667, 0.3333333333}
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