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Simplifying (5 + -6i)(9 + i) = 0 Multiply (5 + -6i) * (9 + i) (5(9 + i) + -6i * (9 + i)) = 0 ((9 * 5 + i * 5) + -6i * (9 + i)) = 0 ((45 + 5i) + -6i * (9 + i)) = 0 (45 + 5i + (9 * -6i + i * -6i)) = 0 (45 + 5i + (-54i + -6i2)) = 0 Combine like terms: 5i + -54i = -49i (45 + -49i + -6i2) = 0 Solving 45 + -49i + -6i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -6i)(9 + i) = 0Subproblem 1
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 = 0.8333333333Subproblem 2
Set the factor '(9 + i)' equal to zero and attempt to solve: Simplifying 9 + i = 0 Solving 9 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + i = 0 + -9 i = 0 + -9 Combine like terms: 0 + -9 = -9 i = -9 Simplifying i = -9Solution
i = {0.8333333333, -9}
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