(1+3i)(3+i)=

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

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

Multiply (1 + 3i) * (3 + i)
(1(3 + i) + 3i * (3 + i)) = 0
((3 * 1 + i * 1) + 3i * (3 + i)) = 0
((3 + 1i) + 3i * (3 + i)) = 0
(3 + 1i + (3 * 3i + i * 3i)) = 0
(3 + 1i + (9i + 3i2)) = 0

Combine like terms: 1i + 9i = 10i
(3 + 10i + 3i2) = 0

Solving
3 + 10i + 3i2 = 0

Solving for variable 'i'.

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

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

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
Subproblem 2
Set the factor '(1 + 3i)' equal to zero and attempt to solve:

Simplifying
1 + 3i = 0

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

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

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

Divide each side by '3'.
i = -0.3333333333

Simplifying
i = -0.3333333333
Solution
i = {-3, -0.3333333333}