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

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

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

Multiply (1 + -2i) * (3 + 4i)
(1(3 + 4i) + -2i * (3 + 4i)) = 0
((3 * 1 + 4i * 1) + -2i * (3 + 4i)) = 0
((3 + 4i) + -2i * (3 + 4i)) = 0
(3 + 4i + (3 * -2i + 4i * -2i)) = 0
(3 + 4i + (-6i + -8i2)) = 0

Combine like terms: 4i + -6i = -2i
(3 + -2i + -8i2) = 0

Solving
3 + -2i + -8i2 = 0

Solving for variable 'i'.

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

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

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Subproblem 2
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
Solution
i = {0.5, -0.75}