(1-z)(i-1)=z(i+1)

Solution for (1-z)(i-1)=z(i+1) equation:

Simplifying
(1 + -1z)(i + -1) = z(i + 1)

Reorder the terms:
(1 + -1z)(-1 + i) = z(i + 1)

Multiply (1 + -1z) * (-1 + i)
(1(-1 + i) + -1z * (-1 + i)) = z(i + 1)
((-1 * 1 + i * 1) + -1z * (-1 + i)) = z(i + 1)
((-1 + 1i) + -1z * (-1 + i)) = z(i + 1)
(-1 + 1i + (-1 * -1z + i * -1z)) = z(i + 1)

Reorder the terms:
(-1 + 1i + (-1iz + 1z)) = z(i + 1)
(-1 + 1i + (-1iz + 1z)) = z(i + 1)
(-1 + 1i + -1iz + 1z) = z(i + 1)

Reorder the terms:
-1 + 1i + -1iz + 1z = z(1 + i)
-1 + 1i + -1iz + 1z = (1 * z + i * z)

Reorder the terms:
-1 + 1i + -1iz + 1z = (iz + 1z)
-1 + 1i + -1iz + 1z = (iz + 1z)

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

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

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

Solving
-1 + 1i + -1iz = iz

Solving for variable 'i'.

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

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

Combine like terms: -1iz + -1iz = -2iz
-1 + 1i + -2iz = iz + -1iz

Combine like terms: iz + -1iz = 0
-1 + 1i + -2iz = 0

Add '1' to each side of the equation.
-1 + 1i + 1 + -2iz = 0 + 1

Reorder the terms:
-1 + 1 + 1i + -2iz = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1i + -2iz = 0 + 1
1i + -2iz = 0 + 1

Combine like terms: 0 + 1 = 1
1i + -2iz = 1

Reorder the terms:
-1 + 1i + -2iz = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 1i + -2iz = 0

The solution to this equation could not be determined.