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Simplifying (9 + -7i)(6 + i) = 0 Multiply (9 + -7i) * (6 + i) (9(6 + i) + -7i * (6 + i)) = 0 ((6 * 9 + i * 9) + -7i * (6 + i)) = 0 ((54 + 9i) + -7i * (6 + i)) = 0 (54 + 9i + (6 * -7i + i * -7i)) = 0 (54 + 9i + (-42i + -7i2)) = 0 Combine like terms: 9i + -42i = -33i (54 + -33i + -7i2) = 0 Solving 54 + -33i + -7i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -7i)(6 + i) = 0Subproblem 1
Set the factor '(9 + -7i)' equal to zero and attempt to solve: Simplifying 9 + -7i = 0 Solving 9 + -7i = 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 + -7i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7i = 0 + -9 -7i = 0 + -9 Combine like terms: 0 + -9 = -9 -7i = -9 Divide each side by '-7'. i = 1.285714286 Simplifying i = 1.285714286Subproblem 2
Set the factor '(6 + i)' equal to zero and attempt to solve: Simplifying 6 + i = 0 Solving 6 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + i = 0 + -6 i = 0 + -6 Combine like terms: 0 + -6 = -6 i = -6 Simplifying i = -6Solution
i = {1.285714286, -6}
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