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Simplifying (5 + 6i)(5 + i) = 0 Multiply (5 + 6i) * (5 + i) (5(5 + i) + 6i * (5 + i)) = 0 ((5 * 5 + i * 5) + 6i * (5 + i)) = 0 ((25 + 5i) + 6i * (5 + i)) = 0 (25 + 5i + (5 * 6i + i * 6i)) = 0 (25 + 5i + (30i + 6i2)) = 0 Combine like terms: 5i + 30i = 35i (25 + 35i + 6i2) = 0 Solving 25 + 35i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + i)(5 + 6i) = 0Subproblem 1
Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5Subproblem 2
Set the factor '(5 + 6i)' equal to zero and attempt to solve: Simplifying 5 + 6i = 0 Solving 5 + 6i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6i = 0 + -5 6i = 0 + -5 Combine like terms: 0 + -5 = -5 6i = -5 Divide each side by '6'. i = -0.8333333333 Simplifying i = -0.8333333333Solution
i = {-5, -0.8333333333}
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