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Simplifying (2 + -1i)(3 + 11i) = 0 Multiply (2 + -1i) * (3 + 11i) (2(3 + 11i) + -1i * (3 + 11i)) = 0 ((3 * 2 + 11i * 2) + -1i * (3 + 11i)) = 0 ((6 + 22i) + -1i * (3 + 11i)) = 0 (6 + 22i + (3 * -1i + 11i * -1i)) = 0 (6 + 22i + (-3i + -11i2)) = 0 Combine like terms: 22i + -3i = 19i (6 + 19i + -11i2) = 0 Solving 6 + 19i + -11i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -1i)(3 + 11i) = 0Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
Set the factor '(3 + 11i)' equal to zero and attempt to solve: Simplifying 3 + 11i = 0 Solving 3 + 11i = 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 + 11i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 11i = 0 + -3 11i = 0 + -3 Combine like terms: 0 + -3 = -3 11i = -3 Divide each side by '11'. i = -0.2727272727 Simplifying i = -0.2727272727Solution
i = {2, -0.2727272727}
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