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Simplifying (6 + -6i)(5 + i) = 0 Multiply (6 + -6i) * (5 + i) (6(5 + i) + -6i * (5 + i)) = 0 ((5 * 6 + i * 6) + -6i * (5 + i)) = 0 ((30 + 6i) + -6i * (5 + i)) = 0 (30 + 6i + (5 * -6i + i * -6i)) = 0 (30 + 6i + (-30i + -6i2)) = 0 Combine like terms: 6i + -30i = -24i (30 + -24i + -6i2) = 0 Solving 30 + -24i + -6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '6'. 6(5 + -4i + -1i2) = 0 Factor a trinomial. 6((1 + -1i)(5 + i)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 2
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 = -5Solution
i = {1, -5}
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