(2+3i)(1+4i)=

Solution for (2+3i)(1+4i)= equation:

Simplifying
(2 + 3i)(1 + 4i) = 0

Multiply (2 + 3i) * (1 + 4i)
(2(1 + 4i) + 3i * (1 + 4i)) = 0
((1 * 2 + 4i * 2) + 3i * (1 + 4i)) = 0
((2 + 8i) + 3i * (1 + 4i)) = 0
(2 + 8i + (1 * 3i + 4i * 3i)) = 0
(2 + 8i + (3i + 12i2)) = 0

Combine like terms: 8i + 3i = 11i
(2 + 11i + 12i2) = 0

Solving
2 + 11i + 12i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + 3i)(1 + 4i) = 0

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

Simplifying
2 + 3i = 0

Solving
2 + 3i = 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 + 3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3i = 0 + -2
3i = 0 + -2

Combine like terms: 0 + -2 = -2
3i = -2

Divide each side by '3'.
i = -0.6666666667

Simplifying
i = -0.6666666667
Subproblem 2
Set the factor '(1 + 4i)' equal to zero and attempt to solve:

Simplifying
1 + 4i = 0

Solving
1 + 4i = 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 + 4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4i = 0 + -1
4i = 0 + -1

Combine like terms: 0 + -1 = -1
4i = -1

Divide each side by '4'.
i = -0.25

Simplifying
i = -0.25
Solution
i = {-0.6666666667, -0.25}