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Simplifying (4 + -6i)(6 + -8i) = 0 Multiply (4 + -6i) * (6 + -8i) (4(6 + -8i) + -6i * (6 + -8i)) = 0 ((6 * 4 + -8i * 4) + -6i * (6 + -8i)) = 0 ((24 + -32i) + -6i * (6 + -8i)) = 0 (24 + -32i + (6 * -6i + -8i * -6i)) = 0 (24 + -32i + (-36i + 48i2)) = 0 Combine like terms: -32i + -36i = -68i (24 + -68i + 48i2) = 0 Solving 24 + -68i + 48i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -17i + 12i2) = 0 Factor a trinomial. 4((2 + -3i)(3 + -4i)) = 0 Ignore the factor 4.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 '(3 + -4i)' equal to zero and attempt to solve: Simplifying 3 + -4i = 0 Solving 3 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4i = 0 + -3 -4i = 0 + -3 Combine like terms: 0 + -3 = -3 -4i = -3 Divide each side by '-4'. i = 0.75 Simplifying i = 0.75Solution
i = {0.6666666667, 0.75}
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