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Simplifying (3 + -1i)(4 + 11i) = 0 Multiply (3 + -1i) * (4 + 11i) (3(4 + 11i) + -1i * (4 + 11i)) = 0 ((4 * 3 + 11i * 3) + -1i * (4 + 11i)) = 0 ((12 + 33i) + -1i * (4 + 11i)) = 0 (12 + 33i + (4 * -1i + 11i * -1i)) = 0 (12 + 33i + (-4i + -11i2)) = 0 Combine like terms: 33i + -4i = 29i (12 + 29i + -11i2) = 0 Solving 12 + 29i + -11i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -1i)(4 + 11i) = 0Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 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 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Subproblem 2
Set the factor '(4 + 11i)' equal to zero and attempt to solve: Simplifying 4 + 11i = 0 Solving 4 + 11i = 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 + 11i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 11i = 0 + -4 11i = 0 + -4 Combine like terms: 0 + -4 = -4 11i = -4 Divide each side by '11'. i = -0.3636363636 Simplifying i = -0.3636363636Solution
i = {3, -0.3636363636}
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