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Simplifying (5 + -3i)(-4 + -6i) = 0 Multiply (5 + -3i) * (-4 + -6i) (5(-4 + -6i) + -3i * (-4 + -6i)) = 0 ((-4 * 5 + -6i * 5) + -3i * (-4 + -6i)) = 0 ((-20 + -30i) + -3i * (-4 + -6i)) = 0 (-20 + -30i + (-4 * -3i + -6i * -3i)) = 0 (-20 + -30i + (12i + 18i2)) = 0 Combine like terms: -30i + 12i = -18i (-20 + -18i + 18i2) = 0 Solving -20 + -18i + 18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -9i + 9i2) = 0 Factor a trinomial. 2((-2 + -3i)(5 + -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 '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667Solution
i = {-0.6666666667, 1.666666667}
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