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Simplifying (-5 + -4i)(5 + -6i) = 0 Multiply (-5 + -4i) * (5 + -6i) (-5(5 + -6i) + -4i * (5 + -6i)) = 0 ((5 * -5 + -6i * -5) + -4i * (5 + -6i)) = 0 ((-25 + 30i) + -4i * (5 + -6i)) = 0 (-25 + 30i + (5 * -4i + -6i * -4i)) = 0 (-25 + 30i + (-20i + 24i2)) = 0 Combine like terms: 30i + -20i = 10i (-25 + 10i + 24i2) = 0 Solving -25 + 10i + 24i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -4i)(5 + -6i) = 0Subproblem 1
Set the factor '(-5 + -4i)' equal to zero and attempt to solve: Simplifying -5 + -4i = 0 Solving -5 + -4i = 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 + -4i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4i = 0 + 5 -4i = 0 + 5 Combine like terms: 0 + 5 = 5 -4i = 5 Divide each side by '-4'. i = -1.25 Simplifying i = -1.25Subproblem 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 = {-1.25, 0.8333333333}
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