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Simplifying (-8 + 4i)(6 + 2i) = 0 Multiply (-8 + 4i) * (6 + 2i) (-8(6 + 2i) + 4i * (6 + 2i)) = 0 ((6 * -8 + 2i * -8) + 4i * (6 + 2i)) = 0 ((-48 + -16i) + 4i * (6 + 2i)) = 0 (-48 + -16i + (6 * 4i + 2i * 4i)) = 0 (-48 + -16i + (24i + 8i2)) = 0 Combine like terms: -16i + 24i = 8i (-48 + 8i + 8i2) = 0 Solving -48 + 8i + 8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '8'. 8(-6 + i + i2) = 0 Factor a trinomial. 8((-3 + -1i)(2 + -1i)) = 0 Ignore the factor 8.Subproblem 1
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 = -3Subproblem 2
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Solution
i = {-3, 2}
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