z^4-r^4=0

Solution for z^4-r^4=0 equation:

Simplifying
z4 + -1r4 = 0

Reorder the terms:
-1r4 + z4 = 0

Solving
-1r4 + z4 = 0

Solving for variable 'r'.

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

Add '-1z4' to each side of the equation.
-1r4 + z4 + -1z4 = 0 + -1z4

Combine like terms: z4 + -1z4 = 0
-1r4 + 0 = 0 + -1z4
-1r4 = 0 + -1z4
Remove the zero:
-1r4 = -1z4

Divide each side by '-1'.
r4 = z4

Simplifying
r4 = z4

Combine like terms: z4 + -1z4 = 0
r4 + -1z4 = 0

Factor a difference between two squares.
(r2 + z2)(r2 + -1z2) = 0

Factor a difference between two squares.
(r2 + z2)((r + z)(r + -1z)) = 0

Subproblem 1
Set the factor '(r2 + z2)' equal to zero and attempt to solve:

Simplifying
r2 + z2 = 0

Solving
r2 + z2 = 0

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

Add '-1z2' to each side of the equation.
r2 + z2 + -1z2 = 0 + -1z2

Combine like terms: z2 + -1z2 = 0
r2 + 0 = 0 + -1z2
r2 = 0 + -1z2
Remove the zero:
r2 = -1z2

Simplifying
r2 = -1z2

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 '(r + z)' equal to zero and attempt to solve:

Simplifying
r + z = 0

Solving
r + z = 0

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

Add '-1z' to each side of the equation.
r + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
r + 0 = 0 + -1z
r = 0 + -1z
Remove the zero:
r = -1z

Simplifying
r = -1z
Subproblem 3
Set the factor '(r + -1z)' equal to zero and attempt to solve:

Simplifying
r + -1z = 0

Solving
r + -1z = 0

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

Add 'z' to each side of the equation.
r + -1z + z = 0 + z

Combine like terms: -1z + z = 0
r + 0 = 0 + z
r = 0 + z
Remove the zero:
r = z

Simplifying
r = z
Solution
r = {-1z, z}