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Simplifying (2 + 6I)(2 + -5I) = 0 Multiply (2 + 6I) * (2 + -5I) (2(2 + -5I) + 6I * (2 + -5I)) = 0 ((2 * 2 + -5I * 2) + 6I * (2 + -5I)) = 0 ((4 + -10I) + 6I * (2 + -5I)) = 0 (4 + -10I + (2 * 6I + -5I * 6I)) = 0 (4 + -10I + (12I + -30I2)) = 0 Combine like terms: -10I + 12I = 2I (4 + 2I + -30I2) = 0 Solving 4 + 2I + -30I2 = 0 Solving for variable 'I'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + I + -15I2) = 0 Factor a trinomial. 2((2 + -5I)(1 + 3I)) = 0 Ignore the factor 2.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 = 0.4Subproblem 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 = {0.4, -0.3333333333}
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