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

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

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

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

Combine like terms: 15i + -1i = 14i
(3 + 14i + -5i2) = 0

Solving
3 + 14i + -5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -1i)(1 + 5i) = 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 '(1 + 5i)' equal to zero and attempt to solve:

Simplifying
1 + 5i = 0

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

Combine like terms: 1 + -1 = 0
0 + 5i = 0 + -1
5i = 0 + -1

Combine like terms: 0 + -1 = -1
5i = -1

Divide each side by '5'.
i = -0.2

Simplifying
i = -0.2
Solution
i = {3, -0.2}