(4-i)-(5+8i)=

Solution for (4-i)-(5+8i)= equation:

Simplifying
(4 + -1i) + -1(5 + 8i) = 0

Remove parenthesis around (4 + -1i)
4 + -1i + -1(5 + 8i) = 0
4 + -1i + (5 * -1 + 8i * -1) = 0
4 + -1i + (-5 + -8i) = 0

Reorder the terms:
4 + -5 + -1i + -8i = 0

Combine like terms: 4 + -5 = -1
-1 + -1i + -8i = 0

Combine like terms: -1i + -8i = -9i
-1 + -9i = 0

Solving
-1 + -9i = 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 + -9i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9i = 0 + 1
-9i = 0 + 1

Combine like terms: 0 + 1 = 1
-9i = 1

Divide each side by '-9'.
i = -0.1111111111

Simplifying
i = -0.1111111111