(1+4i)-(2-6i)=

Solution for (1+4i)-(2-6i)= equation:

Simplifying
(1 + 4i) + -1(2 + -6i) = 0

Remove parenthesis around (1 + 4i)
1 + 4i + -1(2 + -6i) = 0
1 + 4i + (2 * -1 + -6i * -1) = 0
1 + 4i + (-2 + 6i) = 0

Reorder the terms:
1 + -2 + 4i + 6i = 0

Combine like terms: 1 + -2 = -1
-1 + 4i + 6i = 0

Combine like terms: 4i + 6i = 10i
-1 + 10i = 0

Solving
-1 + 10i = 0

Solving for variable 'i'.

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

Add '1' to each side of the equation.
-1 + 1 + 10i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 10i = 0 + 1
10i = 0 + 1

Combine like terms: 0 + 1 = 1
10i = 1

Divide each side by '10'.
i = 0.1

Simplifying
i = 0.1