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Simplifying (4 + 2i)(1 + -1i) = 0 Multiply (4 + 2i) * (1 + -1i) (4(1 + -1i) + 2i * (1 + -1i)) = 0 ((1 * 4 + -1i * 4) + 2i * (1 + -1i)) = 0 ((4 + -4i) + 2i * (1 + -1i)) = 0 (4 + -4i + (1 * 2i + -1i * 2i)) = 0 (4 + -4i + (2i + -2i2)) = 0 Combine like terms: -4i + 2i = -2i (4 + -2i + -2i2) = 0 Solving 4 + -2i + -2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -1i + -1i2) = 0 Factor a trinomial. 2((1 + -1i)(2 + 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 '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {1, -2}
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