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Simplifying (4 + -1i)(2 + -1i) = 0 Multiply (4 + -1i) * (2 + -1i) (4(2 + -1i) + -1i * (2 + -1i)) = 0 ((2 * 4 + -1i * 4) + -1i * (2 + -1i)) = 0 ((8 + -4i) + -1i * (2 + -1i)) = 0 (8 + -4i + (2 * -1i + -1i * -1i)) = 0 (8 + -4i + (-2i + 1i2)) = 0 Combine like terms: -4i + -2i = -6i (8 + -6i + 1i2) = 0 Solving 8 + -6i + 1i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -1i)(4 + -1i) = 0Subproblem 1
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 = 2Subproblem 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 = {2, 4}
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