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Simplifying (4 + -1I)(-6 + -12I) = 0 Multiply (4 + -1I) * (-6 + -12I) (4(-6 + -12I) + -1I * (-6 + -12I)) = 0 ((-6 * 4 + -12I * 4) + -1I * (-6 + -12I)) = 0 ((-24 + -48I) + -1I * (-6 + -12I)) = 0 (-24 + -48I + (-6 * -1I + -12I * -1I)) = 0 (-24 + -48I + (6I + 12I2)) = 0 Combine like terms: -48I + 6I = -42I (-24 + -42I + 12I2) = 0 Solving -24 + -42I + 12I2 = 0 Solving for variable 'I'. Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + -7I + 2I2) = 0 Factor a trinomial. 6((-1 + -2I)(4 + -1I)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -2I)' equal to zero and attempt to solve: Simplifying -1 + -2I = 0 Solving -1 + -2I = 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 + -2I = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2I = 0 + 1 -2I = 0 + 1 Combine like terms: 0 + 1 = 1 -2I = 1 Divide each side by '-2'. I = -0.5 Simplifying I = -0.5Subproblem 2
Set the factor '(4 + -1I)' equal to zero and attempt to solve: Simplifying 4 + -1I = 0 Solving 4 + -1I = 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 + -1I = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1I = 0 + -4 -1I = 0 + -4 Combine like terms: 0 + -4 = -4 -1I = -4 Divide each side by '-1'. I = 4 Simplifying I = 4Solution
I = {-0.5, 4}
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