(-4+7i)(1+i)=

Solution for (-4+7i)(1+i)= equation:

Simplifying
(-4 + 7i)(1 + i) = 0

Multiply (-4 + 7i) * (1 + i)
(-4(1 + i) + 7i * (1 + i)) = 0
((1 * -4 + i * -4) + 7i * (1 + i)) = 0
((-4 + -4i) + 7i * (1 + i)) = 0
(-4 + -4i + (1 * 7i + i * 7i)) = 0
(-4 + -4i + (7i + 7i2)) = 0

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

Solving
-4 + 3i + 7i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-1 + -1i)(4 + -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 '(4 + -7i)' equal to zero and attempt to solve:

Simplifying
4 + -7i = 0

Solving
4 + -7i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -7i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7i = 0 + -4
-7i = 0 + -4

Combine like terms: 0 + -4 = -4
-7i = -4

Divide each side by '-7'.
i = 0.5714285714

Simplifying
i = 0.5714285714
Solution
i = {-1, 0.5714285714}