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Simplifying (z2 + 1)(z2 + -1) = 0 Reorder the terms: (1 + z2)(z2 + -1) = 0 Reorder the terms: (1 + z2)(-1 + z2) = 0 Multiply (1 + z2) * (-1 + z2) (1(-1 + z2) + z2(-1 + z2)) = 0 ((-1 * 1 + z2 * 1) + z2(-1 + z2)) = 0 ((-1 + 1z2) + z2(-1 + z2)) = 0 (-1 + 1z2 + (-1 * z2 + z2 * z2)) = 0 (-1 + 1z2 + (-1z2 + z4)) = 0 Combine like terms: 1z2 + -1z2 = 0 (-1 + 0 + z4) = 0 (-1 + z4) = 0 Solving -1 + z4 = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + z4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + z4 = 0 + 1 z4 = 0 + 1 Combine like terms: 0 + 1 = 1 z4 = 1 Simplifying z4 = 1 Reorder the terms: -1 + z4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + z4 = 0 Factor a difference between two squares. (1 + z2)(-1 + z2) = 0 Factor a difference between two squares. (1 + z2)((1 + z)(-1 + z)) = 0Subproblem 1
Set the factor '(1 + z2)' equal to zero and attempt to solve: Simplifying 1 + z2 = 0 Solving 1 + z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z2 = 0 + -1 z2 = 0 + -1 Combine like terms: 0 + -1 = -1 z2 = -1 Simplifying z2 = -1 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 '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Subproblem 3
Set the factor '(-1 + z)' equal to zero and attempt to solve: Simplifying -1 + z = 0 Solving -1 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + z = 0 + 1 z = 0 + 1 Combine like terms: 0 + 1 = 1 z = 1 Simplifying z = 1Solution
z = {-1, 1}
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