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Simplifying (6 + 8i)(7 + i) = 0 Multiply (6 + 8i) * (7 + i) (6(7 + i) + 8i * (7 + i)) = 0 ((7 * 6 + i * 6) + 8i * (7 + i)) = 0 ((42 + 6i) + 8i * (7 + i)) = 0 (42 + 6i + (7 * 8i + i * 8i)) = 0 (42 + 6i + (56i + 8i2)) = 0 Combine like terms: 6i + 56i = 62i (42 + 62i + 8i2) = 0 Solving 42 + 62i + 8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 31i + 4i2) = 0 Factor a trinomial. 2((7 + i)(3 + 4i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + i)' equal to zero and attempt to solve: Simplifying 7 + i = 0 Solving 7 + i = 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 + i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + i = 0 + -7 i = 0 + -7 Combine like terms: 0 + -7 = -7 i = -7 Simplifying i = -7Subproblem 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 = {-7, -0.75}
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