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Simplifying (-3 + i)(8 + 2i) = 0 Multiply (-3 + i) * (8 + 2i) (-3(8 + 2i) + i(8 + 2i)) = 0 ((8 * -3 + 2i * -3) + i(8 + 2i)) = 0 ((-24 + -6i) + i(8 + 2i)) = 0 (-24 + -6i + (8 * i + 2i * i)) = 0 (-24 + -6i + (8i + 2i2)) = 0 Combine like terms: -6i + 8i = 2i (-24 + 2i + 2i2) = 0 Solving -24 + 2i + 2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + i + i2) = 0 Factor a trinomial. 2((-4 + -1i)(3 + -1i)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 2
Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 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 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Solution
i = {-4, 3}
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