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Simplifying (5 + -6i)(-2 + -5i) = 0 Multiply (5 + -6i) * (-2 + -5i) (5(-2 + -5i) + -6i * (-2 + -5i)) = 0 ((-2 * 5 + -5i * 5) + -6i * (-2 + -5i)) = 0 ((-10 + -25i) + -6i * (-2 + -5i)) = 0 (-10 + -25i + (-2 * -6i + -5i * -6i)) = 0 (-10 + -25i + (12i + 30i2)) = 0 Combine like terms: -25i + 12i = -13i (-10 + -13i + 30i2) = 0 Solving -10 + -13i + 30i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + -5i)(5 + -6i) = 0Subproblem 1
Set the factor '(-2 + -5i)' equal to zero and attempt to solve: Simplifying -2 + -5i = 0 Solving -2 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5i = 0 + 2 -5i = 0 + 2 Combine like terms: 0 + 2 = 2 -5i = 2 Divide each side by '-5'. i = -0.4 Simplifying i = -0.4Subproblem 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 = {-0.4, 0.8333333333}
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