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Simplifying (8 + -2i)(1 + -1i) = 0 Multiply (8 + -2i) * (1 + -1i) (8(1 + -1i) + -2i * (1 + -1i)) = 0 ((1 * 8 + -1i * 8) + -2i * (1 + -1i)) = 0 ((8 + -8i) + -2i * (1 + -1i)) = 0 (8 + -8i + (1 * -2i + -1i * -2i)) = 0 (8 + -8i + (-2i + 2i2)) = 0 Combine like terms: -8i + -2i = -10i (8 + -10i + 2i2) = 0 Solving 8 + -10i + 2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -5i + i2) = 0 Factor a trinomial. 2((1 + -1i)(4 + -1i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 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 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Subproblem 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 = {1, 4}
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