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Simplifying (-6 + -5i)(5 + -6i) = 0 Multiply (-6 + -5i) * (5 + -6i) (-6(5 + -6i) + -5i * (5 + -6i)) = 0 ((5 * -6 + -6i * -6) + -5i * (5 + -6i)) = 0 ((-30 + 36i) + -5i * (5 + -6i)) = 0 (-30 + 36i + (5 * -5i + -6i * -5i)) = 0 (-30 + 36i + (-25i + 30i2)) = 0 Combine like terms: 36i + -25i = 11i (-30 + 11i + 30i2) = 0 Solving -30 + 11i + 30i2 = 0 Solving for variable 'i'. Factor a trinomial. (-6 + -5i)(5 + -6i) = 0Subproblem 1
Set the factor '(-6 + -5i)' equal to zero and attempt to solve: Simplifying -6 + -5i = 0 Solving -6 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5i = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5i = 0 + 6 -5i = 0 + 6 Combine like terms: 0 + 6 = 6 -5i = 6 Divide each side by '-5'. i = -1.2 Simplifying i = -1.2Subproblem 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 = {-1.2, 0.8333333333}
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