(1+4i)(3-5i)=

Solution for (1+4i)(3-5i)= equation:

Simplifying
(1 + 4i)(3 + -5i) = 0

Multiply (1 + 4i) * (3 + -5i)
(1(3 + -5i) + 4i * (3 + -5i)) = 0
((3 * 1 + -5i * 1) + 4i * (3 + -5i)) = 0
((3 + -5i) + 4i * (3 + -5i)) = 0
(3 + -5i + (3 * 4i + -5i * 4i)) = 0
(3 + -5i + (12i + -20i2)) = 0

Combine like terms: -5i + 12i = 7i
(3 + 7i + -20i2) = 0

Solving
3 + 7i + -20i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -5i)(1 + 4i) = 0

Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve:

Simplifying
3 + -5i = 0

Solving
3 + -5i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5i = 0 + -3
-5i = 0 + -3

Combine like terms: 0 + -3 = -3
-5i = -3

Divide each side by '-5'.
i = 0.6

Simplifying
i = 0.6
Subproblem 2
Set the factor '(1 + 4i)' equal to zero and attempt to solve:

Simplifying
1 + 4i = 0

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

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

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

Divide each side by '4'.
i = -0.25

Simplifying
i = -0.25
Solution
i = {0.6, -0.25}