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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 = 2i (-35 + 2i + 48i2) = 0 Solving -35 + 2i + 48i2 = 0 Solving for variable 'i'. Factor a trinomial. (-7 + -8i)(5 + -6i) = 0Subproblem 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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