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Simplifying (4 + -2i)(-2 + -8i) = 0 Multiply (4 + -2i) * (-2 + -8i) (4(-2 + -8i) + -2i * (-2 + -8i)) = 0 ((-2 * 4 + -8i * 4) + -2i * (-2 + -8i)) = 0 ((-8 + -32i) + -2i * (-2 + -8i)) = 0 (-8 + -32i + (-2 * -2i + -8i * -2i)) = 0 (-8 + -32i + (4i + 16i2)) = 0 Combine like terms: -32i + 4i = -28i (-8 + -28i + 16i2) = 0 Solving -8 + -28i + 16i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -7i + 4i2) = 0 Factor a trinomial. 4((-1 + -4i)(2 + -1i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -4i)' equal to zero and attempt to solve: Simplifying -1 + -4i = 0 Solving -1 + -4i = 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 + -4i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4i = 0 + 1 -4i = 0 + 1 Combine like terms: 0 + 1 = 1 -4i = 1 Divide each side by '-4'. i = -0.25 Simplifying i = -0.25Subproblem 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 = {-0.25, 2}
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