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Simplifying (5 + -6i)(6 + 1i) = 0 Multiply (5 + -6i) * (6 + 1i) (5(6 + 1i) + -6i * (6 + 1i)) = 0 ((6 * 5 + 1i * 5) + -6i * (6 + 1i)) = 0 ((30 + 5i) + -6i * (6 + 1i)) = 0 (30 + 5i + (6 * -6i + 1i * -6i)) = 0 (30 + 5i + (-36i + -6i2)) = 0 Combine like terms: 5i + -36i = -31i (30 + -31i + -6i2) = 0 Solving 30 + -31i + -6i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -6i)(6 + 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 '(6 + i)' equal to zero and attempt to solve: Simplifying 6 + i = 0 Solving 6 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + i = 0 + -6 i = 0 + -6 Combine like terms: 0 + -6 = -6 i = -6 Simplifying i = -6Solution
i = {0.8333333333, -6}
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