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

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

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

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

Combine like terms: 3i + -7i = -4i
(3 + -4i + -7i2) = 0

Solving
3 + -4i + -7i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -7i)(1 + i) = 0

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

Simplifying
1 + i = 0

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

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

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

Simplifying
i = -1
Solution
i = {0.4285714286, -1}