i^2-i^6=

Solution for i^2-i^6= equation:

Simplifying
i2 + -1i6 = 0

Solving
i2 + -1i6 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'i2'.
i2(1 + -1i4) = 0

Factor a difference between two squares.
i2((1 + i2)(1 + -1i2)) = 0

Factor a difference between two squares.
i2((1 + i2)((1 + i)(1 + -1i))) = 0

Subproblem 1
Set the factor 'i2' equal to zero and attempt to solve:

Simplifying
i2 = 0

Solving
i2 = 0

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

Simplifying
i2 = 0

Take the square root of each side:
i = {0}
Subproblem 2
Set the factor '(1 + i2)' equal to zero and attempt to solve:

Simplifying
1 + i2 = 0

Solving
1 + i2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + i2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + i2 = 0 + -1
i2 = 0 + -1

Combine like terms: 0 + -1 = -1
i2 = -1

Simplifying
i2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + i)' equal to zero and attempt to solve:

Simplifying
1 + i = 0

Solving
1 + i = 0

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

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

Combine like terms: 1 + -1 = 0
0 + i = 0 + -1
i = 0 + -1

Combine like terms: 0 + -1 = -1
i = -1

Simplifying
i = -1
Subproblem 4
Set the factor '(1 + -1i)' equal to zero and attempt to solve:

Simplifying
1 + -1i = 0

Solving
1 + -1i = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1i = 0 + -1
-1i = 0 + -1

Combine like terms: 0 + -1 = -1
-1i = -1

Divide each side by '-1'.
i = 1

Simplifying
i = 1
Solution
i = {0, -1, 1}