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

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

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

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

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

Solving
-1 + 6i + 7i2 = 0

Solving for variable 'i'.

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

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

Simplifying
-1 + -1i = 0

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

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

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

Divide each side by '-1'.
i = -1

Simplifying
i = -1
Subproblem 2
Set the factor '(1 + -7i)' equal to zero and attempt to solve:

Simplifying
1 + -7i = 0

Solving
1 + -7i = 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 + -7i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7i = 0 + -1
-7i = 0 + -1

Combine like terms: 0 + -1 = -1
-7i = -1

Divide each side by '-7'.
i = 0.1428571429

Simplifying
i = 0.1428571429
Solution
i = {-1, 0.1428571429}