abs(z-2i)=abs(z+4)

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Solution for abs(z-2i)=abs(z+4) equation:


Simplifying
abs(z + -2i) = abs(z + 4)

Reorder the terms:
abs(-2i + z) = abs(z + 4)
(-2i * abs + z * abs) = abs(z + 4)
(-2abis + absz) = abs(z + 4)

Reorder the terms:
-2abis + absz = abs(4 + z)
-2abis + absz = (4 * abs + z * abs)
-2abis + absz = (4abs + absz)

Add '-1absz' to each side of the equation.
-2abis + absz + -1absz = 4abs + absz + -1absz

Combine like terms: absz + -1absz = 0
-2abis + 0 = 4abs + absz + -1absz
-2abis = 4abs + absz + -1absz

Combine like terms: absz + -1absz = 0
-2abis = 4abs + 0
-2abis = 4abs

Solving
-2abis = 4abs

Solving for variable 'a'.

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

Add '-4abs' to each side of the equation.
-2abis + -4abs = 4abs + -4abs

Combine like terms: 4abs + -4abs = 0
-2abis + -4abs = 0

Factor out the Greatest Common Factor (GCF), '-2abs'.
-2abs(i + 2) = 0

Ignore the factor -2.

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 '(i + 2)' equal to zero and attempt to solve: Simplifying i + 2 = 0 Reorder the terms: 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Add '-1i' to each side of the equation. i + -1i = -2 + -1i Combine like terms: i + -1i = 0 0 = -2 + -1i Simplifying 0 = -2 + -1i 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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