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

Solution for (4+5i)(4+1)=0 equation:

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

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

Reorder the terms for easier multiplication:
5(4 + 5i) = 0
(4 * 5 + 5i * 5) = 0
(20 + 25i) = 0

Solving
20 + 25i = 0

Solving for variable 'i'.

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

Add '-20' to each side of the equation.
20 + -20 + 25i = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 25i = 0 + -20
25i = 0 + -20

Combine like terms: 0 + -20 = -20
25i = -20

Divide each side by '25'.
i = -0.8

Simplifying
i = -0.8