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Simplifying (3 + -2i)(4 + 3i) = 0 Multiply (3 + -2i) * (4 + 3i) (3(4 + 3i) + -2i * (4 + 3i)) = 0 ((4 * 3 + 3i * 3) + -2i * (4 + 3i)) = 0 ((12 + 9i) + -2i * (4 + 3i)) = 0 (12 + 9i + (4 * -2i + 3i * -2i)) = 0 (12 + 9i + (-8i + -6i2)) = 0 Combine like terms: 9i + -8i = 1i (12 + 1i + -6i2) = 0 Solving 12 + 1i + -6i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -2i)(4 + 3i) = 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 '(4 + 3i)' equal to zero and attempt to solve: Simplifying 4 + 3i = 0 Solving 4 + 3i = 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 + 3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i = 0 + -4 3i = 0 + -4 Combine like terms: 0 + -4 = -4 3i = -4 Divide each side by '3'. i = -1.333333333 Simplifying i = -1.333333333Solution
i = {1.5, -1.333333333}
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