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Simplifying (6 + 4i)(7 + 8i) = 0 Multiply (6 + 4i) * (7 + 8i) (6(7 + 8i) + 4i * (7 + 8i)) = 0 ((7 * 6 + 8i * 6) + 4i * (7 + 8i)) = 0 ((42 + 48i) + 4i * (7 + 8i)) = 0 (42 + 48i + (7 * 4i + 8i * 4i)) = 0 (42 + 48i + (28i + 32i2)) = 0 Combine like terms: 48i + 28i = 76i (42 + 76i + 32i2) = 0 Solving 42 + 76i + 32i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 38i + 16i2) = 0 Factor a trinomial. 2((3 + 2i)(7 + 8i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 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 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Subproblem 2
Set the factor '(7 + 8i)' equal to zero and attempt to solve: Simplifying 7 + 8i = 0 Solving 7 + 8i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8i = 0 + -7 8i = 0 + -7 Combine like terms: 0 + -7 = -7 8i = -7 Divide each side by '8'. i = -0.875 Simplifying i = -0.875Solution
i = {-1.5, -0.875}
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