(3+i)*(3+i)=

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

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

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

Combine like terms: 3i + 3i = 6i
(9 + 6i + i2) = 0

Solving
9 + 6i + i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + i)(3 + i) = 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 '(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
Solution
i = {-3, -3}