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Simplifying (7 + 2i)(9 + i) = 0 Multiply (7 + 2i) * (9 + i) (7(9 + i) + 2i * (9 + i)) = 0 ((9 * 7 + i * 7) + 2i * (9 + i)) = 0 ((63 + 7i) + 2i * (9 + i)) = 0 (63 + 7i + (9 * 2i + i * 2i)) = 0 (63 + 7i + (18i + 2i2)) = 0 Combine like terms: 7i + 18i = 25i (63 + 25i + 2i2) = 0 Solving 63 + 25i + 2i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + i)(7 + 2i) = 0Subproblem 1
Set the factor '(9 + i)' equal to zero and attempt to solve: Simplifying 9 + i = 0 Solving 9 + i = 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 + i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + i = 0 + -9 i = 0 + -9 Combine like terms: 0 + -9 = -9 i = -9 Simplifying i = -9Subproblem 2
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 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 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Solution
i = {-9, -3.5}
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