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Simplifying (3 + 9I)(8 + -2I) = 0 Multiply (3 + 9I) * (8 + -2I) (3(8 + -2I) + 9I * (8 + -2I)) = 0 ((8 * 3 + -2I * 3) + 9I * (8 + -2I)) = 0 ((24 + -6I) + 9I * (8 + -2I)) = 0 (24 + -6I + (8 * 9I + -2I * 9I)) = 0 (24 + -6I + (72I + -18I2)) = 0 Combine like terms: -6I + 72I = 66I (24 + 66I + -18I2) = 0 Solving 24 + 66I + -18I2 = 0 Solving for variable 'I'. Factor out the Greatest Common Factor (GCF), '6'. 6(4 + 11I + -3I2) = 0 Factor a trinomial. 6((4 + -1I)(1 + 3I)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -1I)' equal to zero and attempt to solve: Simplifying 4 + -1I = 0 Solving 4 + -1I = 0 Move all terms containing I to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1I = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1I = 0 + -4 -1I = 0 + -4 Combine like terms: 0 + -4 = -4 -1I = -4 Divide each side by '-1'. I = 4 Simplifying I = 4Subproblem 2
Set the factor '(1 + 3I)' equal to zero and attempt to solve: Simplifying 1 + 3I = 0 Solving 1 + 3I = 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 + 3I = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3I = 0 + -1 3I = 0 + -1 Combine like terms: 0 + -1 = -1 3I = -1 Divide each side by '3'. I = -0.3333333333 Simplifying I = -0.3333333333Solution
I = {4, -0.3333333333}
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