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Simplifying (3 + 2i)(-5 + 2i) = 0 Multiply (3 + 2i) * (-5 + 2i) (3(-5 + 2i) + 2i * (-5 + 2i)) = 0 ((-5 * 3 + 2i * 3) + 2i * (-5 + 2i)) = 0 ((-15 + 6i) + 2i * (-5 + 2i)) = 0 (-15 + 6i + (-5 * 2i + 2i * 2i)) = 0 (-15 + 6i + (-10i + 4i2)) = 0 Combine like terms: 6i + -10i = -4i (-15 + -4i + 4i2) = 0 Solving -15 + -4i + 4i2 = 0 Solving for variable 'i'. Factor a trinomial. (-3 + -2i)(5 + -2i) = 0Subproblem 1
Set the factor '(-3 + -2i)' equal to zero and attempt to solve: Simplifying -3 + -2i = 0 Solving -3 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2i = 0 + 3 -2i = 0 + 3 Combine like terms: 0 + 3 = 3 -2i = 3 Divide each side by '-2'. i = -1.5 Simplifying i = -1.5Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 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 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Solution
i = {-1.5, 2.5}
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