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Simplifying (-5 + -6i)(7 + 8i) = 0 Multiply (-5 + -6i) * (7 + 8i) (-5(7 + 8i) + -6i * (7 + 8i)) = 0 ((7 * -5 + 8i * -5) + -6i * (7 + 8i)) = 0 ((-35 + -40i) + -6i * (7 + 8i)) = 0 (-35 + -40i + (7 * -6i + 8i * -6i)) = 0 (-35 + -40i + (-42i + -48i2)) = 0 Combine like terms: -40i + -42i = -82i (-35 + -82i + -48i2) = 0 Solving -35 + -82i + -48i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(35 + 82i + 48i2) = 0 Factor a trinomial. -1((7 + 8i)(5 + 6i)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 8i)' equal to zero and attempt to solve: Simplifying 7 + 8i = 0 Solving 7 + 8i = 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 + 8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8i = 0 + -7 8i = 0 + -7 Combine like terms: 0 + -7 = -7 8i = -7 Divide each side by '8'. i = -0.875 Simplifying i = -0.875Subproblem 2
Set the factor '(5 + 6i)' equal to zero and attempt to solve: Simplifying 5 + 6i = 0 Solving 5 + 6i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6i = 0 + -5 6i = 0 + -5 Combine like terms: 0 + -5 = -5 6i = -5 Divide each side by '6'. i = -0.8333333333 Simplifying i = -0.8333333333Solution
i = {-0.875, -0.8333333333}
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