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Simplifying (8 + i)(6 + -1i) = 13 Multiply (8 + i) * (6 + -1i) (8(6 + -1i) + i(6 + -1i)) = 13 ((6 * 8 + -1i * 8) + i(6 + -1i)) = 13 ((48 + -8i) + i(6 + -1i)) = 13 (48 + -8i + (6 * i + -1i * i)) = 13 (48 + -8i + (6i + -1i2)) = 13 Combine like terms: -8i + 6i = -2i (48 + -2i + -1i2) = 13 Solving 48 + -2i + -1i2 = 13 Solving for variable 'i'. Reorder the terms: 48 + -13 + -2i + -1i2 = 13 + -13 Combine like terms: 48 + -13 = 35 35 + -2i + -1i2 = 13 + -13 Combine like terms: 13 + -13 = 0 35 + -2i + -1i2 = 0 Factor a trinomial. (5 + -1i)(7 + i) = 0Subproblem 1
Set the factor '(5 + -1i)' equal to zero and attempt to solve: Simplifying 5 + -1i = 0 Solving 5 + -1i = 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 + -1i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1i = 0 + -5 -1i = 0 + -5 Combine like terms: 0 + -5 = -5 -1i = -5 Divide each side by '-1'. i = 5 Simplifying i = 5Subproblem 2
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 = -7Solution
i = {5, -7}
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