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Simplifying (4 + 11i)(6 + 2i) = 0 Multiply (4 + 11i) * (6 + 2i) (4(6 + 2i) + 11i * (6 + 2i)) = 0 ((6 * 4 + 2i * 4) + 11i * (6 + 2i)) = 0 ((24 + 8i) + 11i * (6 + 2i)) = 0 (24 + 8i + (6 * 11i + 2i * 11i)) = 0 (24 + 8i + (66i + 22i2)) = 0 Combine like terms: 8i + 66i = 74i (24 + 74i + 22i2) = 0 Solving 24 + 74i + 22i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 37i + 11i2) = 0 Factor a trinomial. 2((3 + i)(4 + 11i)) = 0 Ignore the factor 2.Subproblem 1
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 = -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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