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Simplifying (4j2 + 1)(2j + 1)(2j + -1) = 0 Reorder the terms: (1 + 4j2)(2j + 1)(2j + -1) = 0 Reorder the terms: (1 + 4j2)(1 + 2j)(2j + -1) = 0 Reorder the terms: (1 + 4j2)(1 + 2j)(-1 + 2j) = 0 Multiply (1 + 4j2) * (1 + 2j) (1(1 + 2j) + 4j2 * (1 + 2j))(-1 + 2j) = 0 ((1 * 1 + 2j * 1) + 4j2 * (1 + 2j))(-1 + 2j) = 0 ((1 + 2j) + 4j2 * (1 + 2j))(-1 + 2j) = 0 (1 + 2j + (1 * 4j2 + 2j * 4j2))(-1 + 2j) = 0 (1 + 2j + (4j2 + 8j3))(-1 + 2j) = 0 (1 + 2j + 4j2 + 8j3)(-1 + 2j) = 0 Multiply (1 + 2j + 4j2 + 8j3) * (-1 + 2j) (1(-1 + 2j) + 2j * (-1 + 2j) + 4j2 * (-1 + 2j) + 8j3 * (-1 + 2j)) = 0 ((-1 * 1 + 2j * 1) + 2j * (-1 + 2j) + 4j2 * (-1 + 2j) + 8j3 * (-1 + 2j)) = 0 ((-1 + 2j) + 2j * (-1 + 2j) + 4j2 * (-1 + 2j) + 8j3 * (-1 + 2j)) = 0 (-1 + 2j + (-1 * 2j + 2j * 2j) + 4j2 * (-1 + 2j) + 8j3 * (-1 + 2j)) = 0 (-1 + 2j + (-2j + 4j2) + 4j2 * (-1 + 2j) + 8j3 * (-1 + 2j)) = 0 (-1 + 2j + -2j + 4j2 + (-1 * 4j2 + 2j * 4j2) + 8j3 * (-1 + 2j)) = 0 (-1 + 2j + -2j + 4j2 + (-4j2 + 8j3) + 8j3 * (-1 + 2j)) = 0 (-1 + 2j + -2j + 4j2 + -4j2 + 8j3 + (-1 * 8j3 + 2j * 8j3)) = 0 (-1 + 2j + -2j + 4j2 + -4j2 + 8j3 + (-8j3 + 16j4)) = 0 Combine like terms: 2j + -2j = 0 (-1 + 0 + 4j2 + -4j2 + 8j3 + -8j3 + 16j4) = 0 (-1 + 4j2 + -4j2 + 8j3 + -8j3 + 16j4) = 0 Combine like terms: 4j2 + -4j2 = 0 (-1 + 0 + 8j3 + -8j3 + 16j4) = 0 (-1 + 8j3 + -8j3 + 16j4) = 0 Combine like terms: 8j3 + -8j3 = 0 (-1 + 0 + 16j4) = 0 (-1 + 16j4) = 0 Solving -1 + 16j4 = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 16j4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 16j4 = 0 + 1 16j4 = 0 + 1 Combine like terms: 0 + 1 = 1 16j4 = 1 Divide each side by '16'. j4 = 0.0625 Simplifying j4 = 0.0625 Reorder the terms: -0.0625 + j4 = 0.0625 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 -0.0625 + j4 = 0.0000 Factor a difference between two squares. (0.25 + j2)(-0.25 + j2) = 0.0000 Factor a difference between two squares. (0.25 + j2)((0.5 + j)(-0.5 + j)) = 0.0000Subproblem 1
Set the factor '(0.25 + j2)' equal to zero and attempt to solve: Simplifying 0.25 + j2 = 0 Solving 0.25 + j2 = 0 Move all terms containing j to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + j2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + j2 = 0 + -0.25 j2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 j2 = -0.25 Simplifying j2 = -0.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(0.5 + j)' equal to zero and attempt to solve: Simplifying 0.5 + j = 0 Solving 0.5 + j = 0 Move all terms containing j to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + j = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + j = 0 + -0.5 j = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 j = -0.5 Simplifying j = -0.5Subproblem 3
Set the factor '(-0.5 + j)' equal to zero and attempt to solve: Simplifying -0.5 + j = 0 Solving -0.5 + j = 0 Move all terms containing j to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + j = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + j = 0 + 0.5 j = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 j = 0.5 Simplifying j = 0.5Solution
j = {-0.5, 0.5}
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