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Simplifying (11 + -12i)(-4 + 6i) = 0 Multiply (11 + -12i) * (-4 + 6i) (11(-4 + 6i) + -12i * (-4 + 6i)) = 0 ((-4 * 11 + 6i * 11) + -12i * (-4 + 6i)) = 0 ((-44 + 66i) + -12i * (-4 + 6i)) = 0 (-44 + 66i + (-4 * -12i + 6i * -12i)) = 0 (-44 + 66i + (48i + -72i2)) = 0 Combine like terms: 66i + 48i = 114i (-44 + 114i + -72i2) = 0 Solving -44 + 114i + -72i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 57i + -36i2) = 0 Factor a trinomial. 2((-11 + 12i)(2 + -3i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 12i)' equal to zero and attempt to solve: Simplifying -11 + 12i = 0 Solving -11 + 12i = 0 Move all terms containing i to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 12i = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 12i = 0 + 11 12i = 0 + 11 Combine like terms: 0 + 11 = 11 12i = 11 Divide each side by '12'. i = 0.9166666667 Simplifying i = 0.9166666667Subproblem 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 = {0.9166666667, 0.6666666667}
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