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Simplifying (9 + 6I)(7 + -4I) = 0 Multiply (9 + 6I) * (7 + -4I) (9(7 + -4I) + 6I * (7 + -4I)) = 0 ((7 * 9 + -4I * 9) + 6I * (7 + -4I)) = 0 ((63 + -36I) + 6I * (7 + -4I)) = 0 (63 + -36I + (7 * 6I + -4I * 6I)) = 0 (63 + -36I + (42I + -24I2)) = 0 Combine like terms: -36I + 42I = 6I (63 + 6I + -24I2) = 0 Solving 63 + 6I + -24I2 = 0 Solving for variable 'I'. Factor out the Greatest Common Factor (GCF), '3'. 3(21 + 2I + -8I2) = 0 Factor a trinomial. 3((7 + -4I)(3 + 2I)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -4I)' equal to zero and attempt to solve: Simplifying 7 + -4I = 0 Solving 7 + -4I = 0 Move all terms containing I to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4I = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4I = 0 + -7 -4I = 0 + -7 Combine like terms: 0 + -7 = -7 -4I = -7 Divide each side by '-4'. I = 1.75 Simplifying I = 1.75Subproblem 2
Set the factor '(3 + 2I)' equal to zero and attempt to solve: Simplifying 3 + 2I = 0 Solving 3 + 2I = 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 + 2I = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2I = 0 + -3 2I = 0 + -3 Combine like terms: 0 + -3 = -3 2I = -3 Divide each side by '2'. I = -1.5 Simplifying I = -1.5Solution
I = {1.75, -1.5}
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