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Simplifying (2 + 3i)(6 + -8i) = 0 Multiply (2 + 3i) * (6 + -8i) (2(6 + -8i) + 3i * (6 + -8i)) = 0 ((6 * 2 + -8i * 2) + 3i * (6 + -8i)) = 0 ((12 + -16i) + 3i * (6 + -8i)) = 0 (12 + -16i + (6 * 3i + -8i * 3i)) = 0 (12 + -16i + (18i + -24i2)) = 0 Combine like terms: -16i + 18i = 2i (12 + 2i + -24i2) = 0 Solving 12 + 2i + -24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + i + -12i2) = 0 Factor a trinomial. 2((3 + -4i)(2 + 3i)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.75Subproblem 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 = {0.75, -0.6666666667}
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