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Simplifying (3 + I)(5 + I) = 0 Multiply (3 + I) * (5 + I) (3(5 + I) + I(5 + I)) = 0 ((5 * 3 + I * 3) + I(5 + I)) = 0 ((15 + 3I) + I(5 + I)) = 0 (15 + 3I + (5 * I + I * I)) = 0 (15 + 3I + (5I + I2)) = 0 Combine like terms: 3I + 5I = 8I (15 + 8I + I2) = 0 Solving 15 + 8I + I2 = 0 Solving for variable 'I'. Factor a trinomial. (5 + I)(3 + I) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(3 + I)' equal to zero and attempt to solve: Simplifying 3 + I = 0 Solving 3 + I = 0 Move all terms containing I to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + I = 0 + -3 Combine like terms: 3 + -3 = 0 0 + I = 0 + -3 I = 0 + -3 Combine like terms: 0 + -3 = -3 I = -3 Simplifying I = -3Solution
I = {-5, -3}
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