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Simplifying (3 + 2i)(4 + -5i) = 0 Multiply (3 + 2i) * (4 + -5i) (3(4 + -5i) + 2i * (4 + -5i)) = 0 ((4 * 3 + -5i * 3) + 2i * (4 + -5i)) = 0 ((12 + -15i) + 2i * (4 + -5i)) = 0 (12 + -15i + (4 * 2i + -5i * 2i)) = 0 (12 + -15i + (8i + -10i2)) = 0 Combine like terms: -15i + 8i = -7i (12 + -7i + -10i2) = 0 Solving 12 + -7i + -10i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -5i)(3 + 2i) = 0Subproblem 1
Set the factor '(4 + -5i)' equal to zero and attempt to solve: Simplifying 4 + -5i = 0 Solving 4 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5i = 0 + -4 -5i = 0 + -4 Combine like terms: 0 + -4 = -4 -5i = -4 Divide each side by '-5'. i = 0.8 Simplifying i = 0.8Subproblem 2
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 = -1.5Solution
i = {0.8, -1.5}
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