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