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Simplifying (5 + 8i)(3 + i) = 0 Multiply (5 + 8i) * (3 + i) (5(3 + i) + 8i * (3 + i)) = 0 ((3 * 5 + i * 5) + 8i * (3 + i)) = 0 ((15 + 5i) + 8i * (3 + i)) = 0 (15 + 5i + (3 * 8i + i * 8i)) = 0 (15 + 5i + (24i + 8i2)) = 0 Combine like terms: 5i + 24i = 29i (15 + 29i + 8i2) = 0 Solving 15 + 29i + 8i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + i)(5 + 8i) = 0Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 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 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Subproblem 2
Set the factor '(5 + 8i)' equal to zero and attempt to solve: Simplifying 5 + 8i = 0 Solving 5 + 8i = 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 + 8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8i = 0 + -5 8i = 0 + -5 Combine like terms: 0 + -5 = -5 8i = -5 Divide each side by '8'. i = -0.625 Simplifying i = -0.625Solution
i = {-3, -0.625}
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