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Simplifying (3 + 6I)(5 + -1I) = 0 Multiply (3 + 6I) * (5 + -1I) (3(5 + -1I) + 6I * (5 + -1I)) = 0 ((5 * 3 + -1I * 3) + 6I * (5 + -1I)) = 0 ((15 + -3I) + 6I * (5 + -1I)) = 0 (15 + -3I + (5 * 6I + -1I * 6I)) = 0 (15 + -3I + (30I + -6I2)) = 0 Combine like terms: -3I + 30I = 27I (15 + 27I + -6I2) = 0 Solving 15 + 27I + -6I2 = 0 Solving for variable 'I'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 9I + -2I2) = 0 Factor a trinomial. 3((5 + -1I)(1 + 2I)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -1I)' equal to zero and attempt to solve: Simplifying 5 + -1I = 0 Solving 5 + -1I = 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 + -1I = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1I = 0 + -5 -1I = 0 + -5 Combine like terms: 0 + -5 = -5 -1I = -5 Divide each side by '-1'. I = 5 Simplifying I = 5Subproblem 2
Set the factor '(1 + 2I)' equal to zero and attempt to solve: Simplifying 1 + 2I = 0 Solving 1 + 2I = 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 + 2I = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2I = 0 + -1 2I = 0 + -1 Combine like terms: 0 + -1 = -1 2I = -1 Divide each side by '2'. I = -0.5 Simplifying I = -0.5Solution
I = {5, -0.5}
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