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Simplifying abs(z + 2) = abs(z + 3i) Reorder the terms: abs(2 + z) = abs(z + 3i) (2 * abs + z * abs) = abs(z + 3i) (2abs + absz) = abs(z + 3i) Reorder the terms: 2abs + absz = abs(3i + z) 2abs + absz = (3i * abs + z * abs) 2abs + absz = (3abis + absz) Add '-1absz' to each side of the equation. 2abs + absz + -1absz = 3abis + absz + -1absz Combine like terms: absz + -1absz = 0 2abs + 0 = 3abis + absz + -1absz 2abs = 3abis + absz + -1absz Combine like terms: absz + -1absz = 0 2abs = 3abis + 0 2abs = 3abis Solving 2abs = 3abis Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3abis' to each side of the equation. -3abis + 2abs = 3abis + -3abis Combine like terms: 3abis + -3abis = 0 -3abis + 2abs = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-3i + 2) = 0Subproblem 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 '(-3i + 2)' equal to zero and attempt to solve: Simplifying -3i + 2 = 0 Reorder the terms: 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Add '3i' to each side of the equation. -3i + 3i = -2 + 3i Combine like terms: -3i + 3i = 0 0 = -2 + 3i Simplifying 0 = -2 + 3i 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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