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