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Simplifying (2 + -2i)(8 + i) = 0 Multiply (2 + -2i) * (8 + i) (2(8 + i) + -2i * (8 + i)) = 0 ((8 * 2 + i * 2) + -2i * (8 + i)) = 0 ((16 + 2i) + -2i * (8 + i)) = 0 (16 + 2i + (8 * -2i + i * -2i)) = 0 (16 + 2i + (-16i + -2i2)) = 0 Combine like terms: 2i + -16i = -14i (16 + -14i + -2i2) = 0 Solving 16 + -14i + -2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -7i + -1i2) = 0 Factor a trinomial. 2((1 + -1i)(8 + i)) = 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 '(8 + i)' equal to zero and attempt to solve: Simplifying 8 + i = 0 Solving 8 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + i = 0 + -8 i = 0 + -8 Combine like terms: 0 + -8 = -8 i = -8 Simplifying i = -8Solution
i = {1, -8}
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