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Simplifying (8 + -4i)(-3 + 9i) = 0 Multiply (8 + -4i) * (-3 + 9i) (8(-3 + 9i) + -4i * (-3 + 9i)) = 0 ((-3 * 8 + 9i * 8) + -4i * (-3 + 9i)) = 0 ((-24 + 72i) + -4i * (-3 + 9i)) = 0 (-24 + 72i + (-3 * -4i + 9i * -4i)) = 0 (-24 + 72i + (12i + -36i2)) = 0 Combine like terms: 72i + 12i = 84i (-24 + 84i + -36i2) = 0 Solving -24 + 84i + -36i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '12'. 12(-2 + 7i + -3i2) = 0 Factor a trinomial. 12((-2 + i)(1 + -3i)) = 0 Ignore the factor 12.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 '(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 = {2, 0.3333333333}
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