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Simplifying (2 + -5I)(3 + -4I) = 0 Multiply (2 + -5I) * (3 + -4I) (2(3 + -4I) + -5I * (3 + -4I)) = 0 ((3 * 2 + -4I * 2) + -5I * (3 + -4I)) = 0 ((6 + -8I) + -5I * (3 + -4I)) = 0 (6 + -8I + (3 * -5I + -4I * -5I)) = 0 (6 + -8I + (-15I + 20I^{2})) = 0 Combine like terms: -8I + -15I = -23I (6 + -23I + 20I^{2}) = 0 Solving 6 + -23I + 20I^{2}= 0 Solving for variable 'I'. Factor a trinomial. (2 + -5I)(3 + -4I) = 0## Subproblem 1

Set the factor '(2 + -5I)' equal to zero and attempt to solve: Simplifying 2 + -5I = 0 Solving 2 + -5I = 0 Move all terms containing I to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5I = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5I = 0 + -2 -5I = 0 + -2 Combine like terms: 0 + -2 = -2 -5I = -2 Divide each side by '-5'. I = 0.4 Simplifying I = 0.4## Subproblem 2

Set the factor '(3 + -4I)' equal to zero and attempt to solve: Simplifying 3 + -4I = 0 Solving 3 + -4I = 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 + -4I = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4I = 0 + -3 -4I = 0 + -3 Combine like terms: 0 + -3 = -3 -4I = -3 Divide each side by '-4'. I = 0.75 Simplifying I = 0.75## Solution

I = {0.4, 0.75}

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