abs(z-5)=abs(z-4*i)

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Solution for abs(z-5)=abs(z-4*i) equation:


Simplifying
abs(z + -5) = abs(z + -4i)

Reorder the terms:
abs(-5 + z) = abs(z + -4i)
(-5 * abs + z * abs) = abs(z + -4i)
(-5abs + absz) = abs(z + -4i)

Reorder the terms:
-5abs + absz = abs(-4i + z)
-5abs + absz = (-4i * abs + z * abs)
-5abs + absz = (-4abis + absz)

Add '-1absz' to each side of the equation.
-5abs + absz + -1absz = -4abis + absz + -1absz

Combine like terms: absz + -1absz = 0
-5abs + 0 = -4abis + absz + -1absz
-5abs = -4abis + absz + -1absz

Combine like terms: absz + -1absz = 0
-5abs = -4abis + 0
-5abs = -4abis

Solving
-5abs = -4abis

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4abis' to each side of the equation.
4abis + -5abs = -4abis + 4abis

Combine like terms: -4abis + 4abis = 0
4abis + -5abs = 0

Factor out the Greatest Common Factor (GCF), 'abs'.
abs(4i + -5) = 0

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 '(4i + -5)' equal to zero and attempt to solve: Simplifying 4i + -5 = 0 Reorder the terms: -5 + 4i = 0 Solving -5 + 4i = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4i = 0 + 5 4i = 0 + 5 Combine like terms: 0 + 5 = 5 4i = 5 Add '-4i' to each side of the equation. 4i + -4i = 5 + -4i Combine like terms: 4i + -4i = 0 0 = 5 + -4i Simplifying 0 = 5 + -4i 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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