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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. (4 + -3i)(3 + 2i) = 0Subproblem 1
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 = 1.333333333Subproblem 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 = {1.333333333, -1.5}
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