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Simplifying (4 + -5I)(3 + -3I) = 0 Multiply (4 + -5I) * (3 + -3I) (4(3 + -3I) + -5I * (3 + -3I)) = 0 ((3 * 4 + -3I * 4) + -5I * (3 + -3I)) = 0 ((12 + -12I) + -5I * (3 + -3I)) = 0 (12 + -12I + (3 * -5I + -3I * -5I)) = 0 (12 + -12I + (-15I + 15I2)) = 0 Combine like terms: -12I + -15I = -27I (12 + -27I + 15I2) = 0 Solving 12 + -27I + 15I2 = 0 Solving for variable 'I'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -9I + 5I2) = 0 Factor a trinomial. 3((4 + -5I)(1 + -1I)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -5I)' equal to zero and attempt to solve: Simplifying 4 + -5I = 0 Solving 4 + -5I = 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 + -5I = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5I = 0 + -4 -5I = 0 + -4 Combine like terms: 0 + -4 = -4 -5I = -4 Divide each side by '-5'. I = 0.8 Simplifying I = 0.8Subproblem 2
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 = 1Solution
I = {0.8, 1}
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