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Simplifying abs(z + 4 + -2i) = abs(z + -8 + 2i) Reorder the terms: abs(4 + -2i + z) = abs(z + -8 + 2i) (4 * abs + -2i * abs + z * abs) = abs(z + -8 + 2i) Reorder the terms: (-2abis + 4abs + absz) = abs(z + -8 + 2i) (-2abis + 4abs + absz) = abs(z + -8 + 2i) Reorder the terms: -2abis + 4abs + absz = abs(-8 + 2i + z) -2abis + 4abs + absz = (-8 * abs + 2i * abs + z * abs) Reorder the terms: -2abis + 4abs + absz = (2abis + -8abs + absz) -2abis + 4abs + absz = (2abis + -8abs + absz) Add '-1absz' to each side of the equation. -2abis + 4abs + absz + -1absz = 2abis + -8abs + absz + -1absz Combine like terms: absz + -1absz = 0 -2abis + 4abs + 0 = 2abis + -8abs + absz + -1absz -2abis + 4abs = 2abis + -8abs + absz + -1absz Combine like terms: absz + -1absz = 0 -2abis + 4abs = 2abis + -8abs + 0 -2abis + 4abs = 2abis + -8abs Solving -2abis + 4abs = 2abis + -8abs Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2abis' to each side of the equation. -2abis + -2abis + 4abs = 2abis + -2abis + -8abs Combine like terms: -2abis + -2abis = -4abis -4abis + 4abs = 2abis + -2abis + -8abs Combine like terms: 2abis + -2abis = 0 -4abis + 4abs = 0 + -8abs -4abis + 4abs = -8abs Add '8abs' to each side of the equation. -4abis + 4abs + 8abs = -8abs + 8abs Combine like terms: 4abs + 8abs = 12abs -4abis + 12abs = -8abs + 8abs Combine like terms: -8abs + 8abs = 0 -4abis + 12abs = 0 Factor out the Greatest Common Factor (GCF), '4abs'. 4abs(-1i + 3) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'abs' equal to zero and attempt to solve: Simplifying abs = 0 Solving abs = 0 Move all terms containing a to the left, all other terms to the right. Simplifying abs = 0 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 '(-1i + 3)' equal to zero and attempt to solve: Simplifying -1i + 3 = 0 Reorder the terms: 3 + -1i = 0 Solving 3 + -1i = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Add 'i' to each side of the equation. -1i + i = -3 + i Combine like terms: -1i + i = 0 0 = -3 + i Simplifying 0 = -3 + i The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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