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Simplifying (7 + 6i)(3 + i) = 0 Multiply (7 + 6i) * (3 + i) (7(3 + i) + 6i * (3 + i)) = 0 ((3 * 7 + i * 7) + 6i * (3 + i)) = 0 ((21 + 7i) + 6i * (3 + i)) = 0 (21 + 7i + (3 * 6i + i * 6i)) = 0 (21 + 7i + (18i + 6i2)) = 0 Combine like terms: 7i + 18i = 25i (21 + 25i + 6i2) = 0 Solving 21 + 25i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + i)(7 + 6i) = 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 '(7 + 6i)' equal to zero and attempt to solve: Simplifying 7 + 6i = 0 Solving 7 + 6i = 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 + 6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6i = 0 + -7 6i = 0 + -7 Combine like terms: 0 + -7 = -7 6i = -7 Divide each side by '6'. i = -1.166666667 Simplifying i = -1.166666667Solution
i = {-3, -1.166666667}
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