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Simplifying (9 + 8i)(7 + i) = 0 Multiply (9 + 8i) * (7 + i) (9(7 + i) + 8i * (7 + i)) = 0 ((7 * 9 + i * 9) + 8i * (7 + i)) = 0 ((63 + 9i) + 8i * (7 + i)) = 0 (63 + 9i + (7 * 8i + i * 8i)) = 0 (63 + 9i + (56i + 8i2)) = 0 Combine like terms: 9i + 56i = 65i (63 + 65i + 8i2) = 0 Solving 63 + 65i + 8i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + i)(9 + 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 '(9 + 8i)' equal to zero and attempt to solve: Simplifying 9 + 8i = 0 Solving 9 + 8i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 8i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8i = 0 + -9 8i = 0 + -9 Combine like terms: 0 + -9 = -9 8i = -9 Divide each side by '8'. i = -1.125 Simplifying i = -1.125Solution
i = {-7, -1.125}
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