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Simplifying (7 + -6i)(8 + -5i) = 0 Multiply (7 + -6i) * (8 + -5i) (7(8 + -5i) + -6i * (8 + -5i)) = 0 ((8 * 7 + -5i * 7) + -6i * (8 + -5i)) = 0 ((56 + -35i) + -6i * (8 + -5i)) = 0 (56 + -35i + (8 * -6i + -5i * -6i)) = 0 (56 + -35i + (-48i + 30i2)) = 0 Combine like terms: -35i + -48i = -83i (56 + -83i + 30i2) = 0 Solving 56 + -83i + 30i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + -6i)(8 + -5i) = 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 '(8 + -5i)' equal to zero and attempt to solve: Simplifying 8 + -5i = 0 Solving 8 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5i = 0 + -8 -5i = 0 + -8 Combine like terms: 0 + -8 = -8 -5i = -8 Divide each side by '-5'. i = 1.6 Simplifying i = 1.6Solution
i = {1.166666667, 1.6}
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