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Simplifying 2abs(z + -3i) = abs(z + 3i) Reorder the terms: 2abs(-3i + z) = abs(z + 3i) (-3i * 2abs + z * 2abs) = abs(z + 3i) (-6abis + 2absz) = abs(z + 3i) Reorder the terms: -6abis + 2absz = abs(3i + z) -6abis + 2absz = (3i * abs + z * abs) -6abis + 2absz = (3abis + absz) Solving -6abis + 2absz = 3abis + absz 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. -6abis + -3abis + 2absz = 3abis + -3abis + absz Combine like terms: -6abis + -3abis = -9abis -9abis + 2absz = 3abis + -3abis + absz Combine like terms: 3abis + -3abis = 0 -9abis + 2absz = 0 + absz -9abis + 2absz = absz Add '-1absz' to each side of the equation. -9abis + 2absz + -1absz = absz + -1absz Combine like terms: 2absz + -1absz = 1absz -9abis + 1absz = absz + -1absz Combine like terms: absz + -1absz = 0 -9abis + 1absz = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(-9i + z) = 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 '(-9i + z)' equal to zero and attempt to solve: Simplifying -9i + z = 0 Solving -9i + z = 0 Move all terms containing a to the left, all other terms to the right. Add '9i' to each side of the equation. -9i + 9i + z = 0 + 9i Combine like terms: -9i + 9i = 0 0 + z = 0 + 9i z = 0 + 9i Remove the zero: z = 9i Add '-1z' to each side of the equation. z + -1z = 9i + -1z Combine like terms: z + -1z = 0 0 = 9i + -1z Simplifying 0 = 9i + -1z 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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