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Simplifying (5 + 6i)(-2 + 3i) = 0 Multiply (5 + 6i) * (-2 + 3i) (5(-2 + 3i) + 6i * (-2 + 3i)) = 0 ((-2 * 5 + 3i * 5) + 6i * (-2 + 3i)) = 0 ((-10 + 15i) + 6i * (-2 + 3i)) = 0 (-10 + 15i + (-2 * 6i + 3i * 6i)) = 0 (-10 + 15i + (-12i + 18i2)) = 0 Combine like terms: 15i + -12i = 3i (-10 + 3i + 18i2) = 0 Solving -10 + 3i + 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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