(7+2i)-(1-4i)=

Solution for (7+2i)-(1-4i)= equation:

Simplifying
(7 + 2i) + -1(1 + -4i) = 0

Remove parenthesis around (7 + 2i)
7 + 2i + -1(1 + -4i) = 0
7 + 2i + (1 * -1 + -4i * -1) = 0
7 + 2i + (-1 + 4i) = 0

Reorder the terms:
7 + -1 + 2i + 4i = 0

Combine like terms: 7 + -1 = 6
6 + 2i + 4i = 0

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

Solving
6 + 6i = 0

Solving for variable 'i'.

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

Add '-6' to each side of the equation.
6 + -6 + 6i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 6i = 0 + -6
6i = 0 + -6

Combine like terms: 0 + -6 = -6
6i = -6

Divide each side by '6'.
i = -1

Simplifying
i = -1