(3+7i)(1-2i)=

Solution for (3+7i)(1-2i)= equation:

Simplifying
(3 + 7i)(1 + -2i) = 0

Multiply (3 + 7i) * (1 + -2i)
(3(1 + -2i) + 7i * (1 + -2i)) = 0
((1 * 3 + -2i * 3) + 7i * (1 + -2i)) = 0
((3 + -6i) + 7i * (1 + -2i)) = 0
(3 + -6i + (1 * 7i + -2i * 7i)) = 0
(3 + -6i + (7i + -14i2)) = 0

Combine like terms: -6i + 7i = 1i
(3 + 1i + -14i2) = 0

Solving
3 + 1i + -14i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(1 + -2i)(3 + 7i) = 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 + 7i)' equal to zero and attempt to solve:

Simplifying
3 + 7i = 0

Solving
3 + 7i = 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 + 7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7i = 0 + -3
7i = 0 + -3

Combine like terms: 0 + -3 = -3
7i = -3

Divide each side by '7'.
i = -0.4285714286

Simplifying
i = -0.4285714286
Solution
i = {0.5, -0.4285714286}