(3+4i)(2+11i)=

Solution for (3+4i)(2+11i)= equation:

Simplifying
(3 + 4i)(2 + 11i) = 0

Multiply (3 + 4i) * (2 + 11i)
(3(2 + 11i) + 4i * (2 + 11i)) = 0
((2 * 3 + 11i * 3) + 4i * (2 + 11i)) = 0
((6 + 33i) + 4i * (2 + 11i)) = 0
(6 + 33i + (2 * 4i + 11i * 4i)) = 0
(6 + 33i + (8i + 44i2)) = 0

Combine like terms: 33i + 8i = 41i
(6 + 41i + 44i2) = 0

Solving
6 + 41i + 44i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + 4i)(2 + 11i) = 0

Subproblem 1
Set the factor '(3 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Subproblem 2
Set the factor '(2 + 11i)' equal to zero and attempt to solve:

Simplifying
2 + 11i = 0

Solving
2 + 11i = 0

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

Add '-2' to each side of the equation.
2 + -2 + 11i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 11i = 0 + -2
11i = 0 + -2

Combine like terms: 0 + -2 = -2
11i = -2

Divide each side by '11'.
i = -0.1818181818

Simplifying
i = -0.1818181818
Solution
i = {-0.75, -0.1818181818}