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Simplifying (7 + -6i)(1 + i) = 0 Multiply (7 + -6i) * (1 + i) (7(1 + i) + -6i * (1 + i)) = 0 ((1 * 7 + i * 7) + -6i * (1 + i)) = 0 ((7 + 7i) + -6i * (1 + i)) = 0 (7 + 7i + (1 * -6i + i * -6i)) = 0 (7 + 7i + (-6i + -6i2)) = 0 Combine like terms: 7i + -6i = 1i (7 + 1i + -6i2) = 0 Solving 7 + 1i + -6i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -6i)(1 + i) = 0Subproblem 1
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 = 1.166666667Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {1.166666667, -1}
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