z^4=4

Solution for z^4=4 equation:

Simplifying
z4 = 4

Solving
z4 = 4

Solving for variable 'z'.

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

Simplifying
z4 = 4

Reorder the terms:
-4 + z4 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + z4 = 0

Factor a difference between two squares.
(2 + z2)(-2 + z2) = 0

Subproblem 1
Set the factor '(2 + z2)' equal to zero and attempt to solve:

Simplifying
2 + z2 = 0

Solving
2 + z2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z2 = 0 + -2
z2 = 0 + -2

Combine like terms: 0 + -2 = -2
z2 = -2

Simplifying
z2 = -2

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 '(-2 + z2)' equal to zero and attempt to solve:

Simplifying
-2 + z2 = 0

Solving
-2 + z2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + z2 = 0 + 2
z2 = 0 + 2

Combine like terms: 0 + 2 = 2
z2 = 2

Simplifying
z2 = 2

Take the square root of each side:
z = {-1.414213562, 1.414213562}
Solution
z = {-1.414213562, 1.414213562}