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Simplifying (5 + -2i)(3 + 4i) = 0 Multiply (5 + -2i) * (3 + 4i) (5(3 + 4i) + -2i * (3 + 4i)) = 0 ((3 * 5 + 4i * 5) + -2i * (3 + 4i)) = 0 ((15 + 20i) + -2i * (3 + 4i)) = 0 (15 + 20i + (3 * -2i + 4i * -2i)) = 0 (15 + 20i + (-6i + -8i2)) = 0 Combine like terms: 20i + -6i = 14i (15 + 14i + -8i2) = 0 Solving 15 + 14i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -2i)(3 + 4i) = 0Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 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 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {2.5, -0.75}
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