(4-5i)(1+i)=

Solution for (4-5i)(1+i)= equation:

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

Multiply (4 + -5i) * (1 + i)
(4(1 + i) + -5i * (1 + i)) = 0
((1 * 4 + i * 4) + -5i * (1 + i)) = 0
((4 + 4i) + -5i * (1 + i)) = 0
(4 + 4i + (1 * -5i + i * -5i)) = 0
(4 + 4i + (-5i + -5i2)) = 0

Combine like terms: 4i + -5i = -1i
(4 + -1i + -5i2) = 0

Solving
4 + -1i + -5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + -5i)(1 + i) = 0

Subproblem 1
Set the factor '(4 + -5i)' equal to zero and attempt to solve:

Simplifying
4 + -5i = 0

Solving
4 + -5i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5i = 0 + -4

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

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

Divide each side by '-5'.
i = 0.8

Simplifying
i = 0.8
Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve:

Simplifying
1 + i = 0

Solving
1 + i = 0

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

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

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

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

Simplifying
i = -1
Solution
i = {0.8, -1}