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Simplifying (3 + 8i)(7 + i) = 0 Multiply (3 + 8i) * (7 + i) (3(7 + i) + 8i * (7 + i)) = 0 ((7 * 3 + i * 3) + 8i * (7 + i)) = 0 ((21 + 3i) + 8i * (7 + i)) = 0 (21 + 3i + (7 * 8i + i * 8i)) = 0 (21 + 3i + (56i + 8i2)) = 0 Combine like terms: 3i + 56i = 59i (21 + 59i + 8i2) = 0 Solving 21 + 59i + 8i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + i)(3 + 8i) = 0Subproblem 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 + 8i)' equal to zero and attempt to solve: Simplifying 3 + 8i = 0 Solving 3 + 8i = 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 + 8i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8i = 0 + -3 8i = 0 + -3 Combine like terms: 0 + -3 = -3 8i = -3 Divide each side by '8'. i = -0.375 Simplifying i = -0.375Solution
i = {-7, -0.375}
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