(3+7i)(4-5i)=

Solution for (3+7i)(4-5i)= equation:

Simplifying
(3 + 7i)(4 + -5i) = 0

Multiply (3 + 7i) * (4 + -5i)
(3(4 + -5i) + 7i * (4 + -5i)) = 0
((4 * 3 + -5i * 3) + 7i * (4 + -5i)) = 0
((12 + -15i) + 7i * (4 + -5i)) = 0
(12 + -15i + (4 * 7i + -5i * 7i)) = 0
(12 + -15i + (28i + -35i2)) = 0

Combine like terms: -15i + 28i = 13i
(12 + 13i + -35i2) = 0

Solving
12 + 13i + -35i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + -5i)(3 + 7i) = 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 '(3 + 7i)' equal to zero and attempt to solve:

Simplifying
3 + 7i = 0

Solving
3 + 7i = 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 + 7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7i = 0 + -3
7i = 0 + -3

Combine like terms: 0 + -3 = -3
7i = -3

Divide each side by '7'.
i = -0.4285714286

Simplifying
i = -0.4285714286
Solution
i = {0.8, -0.4285714286}