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

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

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

Reorder the terms:
(2 + z) = (z + -2i)

Remove parenthesis around (2 + z)
2 + z = (z + -2i)

Reorder the terms:
2 + z = (-2i + z)

Remove parenthesis around (-2i + z)
2 + z = -2i + z

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

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

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

Solving
2 = -2i

Solving for variable 'i'.

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

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

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

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

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

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

Divide each side by '2'.
i = -1

Simplifying
i = -1