(5+2i)(3-i)=

Solution for (5+2i)(3-i)= equation:

Simplifying
(5 + 2i)(3 + -1i) = 0

Multiply (5 + 2i) * (3 + -1i)
(5(3 + -1i) + 2i * (3 + -1i)) = 0
((3 * 5 + -1i * 5) + 2i * (3 + -1i)) = 0
((15 + -5i) + 2i * (3 + -1i)) = 0
(15 + -5i + (3 * 2i + -1i * 2i)) = 0
(15 + -5i + (6i + -2i2)) = 0

Combine like terms: -5i + 6i = 1i
(15 + 1i + -2i2) = 0

Solving
15 + 1i + -2i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -1i)(5 + 2i) = 0

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

Simplifying
3 + -1i = 0

Solving
3 + -1i = 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 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Subproblem 2
Set the factor '(5 + 2i)' equal to zero and attempt to solve:

Simplifying
5 + 2i = 0

Solving
5 + 2i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2i = 0 + -5
2i = 0 + -5

Combine like terms: 0 + -5 = -5
2i = -5

Divide each side by '2'.
i = -2.5

Simplifying
i = -2.5
Solution
i = {3, -2.5}