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Simplifying (2 + -3i)(-5 + 6i) = 0 Multiply (2 + -3i) * (-5 + 6i) (2(-5 + 6i) + -3i * (-5 + 6i)) = 0 ((-5 * 2 + 6i * 2) + -3i * (-5 + 6i)) = 0 ((-10 + 12i) + -3i * (-5 + 6i)) = 0 (-10 + 12i + (-5 * -3i + 6i * -3i)) = 0 (-10 + 12i + (15i + -18i2)) = 0 Combine like terms: 12i + 15i = 27i (-10 + 27i + -18i2) = 0 Solving -10 + 27i + -18i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + 6i)(2 + -3i) = 0Subproblem 1
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 = 0.8333333333Subproblem 2
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 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 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Solution
i = {0.8333333333, 0.6666666667}
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