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

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

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

Multiply (-1 + -4i) * (1 + 4i)
(-1(1 + 4i) + -4i * (1 + 4i)) = 0
((1 * -1 + 4i * -1) + -4i * (1 + 4i)) = 0
((-1 + -4i) + -4i * (1 + 4i)) = 0
(-1 + -4i + (1 * -4i + 4i * -4i)) = 0
(-1 + -4i + (-4i + -16i2)) = 0

Combine like terms: -4i + -4i = -8i
(-1 + -8i + -16i2) = 0

Solving
-1 + -8i + -16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 8i + 16i2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 4i)' equal to zero and attempt to solve:

Simplifying
1 + 4i = 0

Solving
1 + 4i = 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 + 4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4i = 0 + -1
4i = 0 + -1

Combine like terms: 0 + -1 = -1
4i = -1

Divide each side by '4'.
i = -0.25

Simplifying
i = -0.25
Subproblem 2
Set the factor '(1 + 4i)' equal to zero and attempt to solve:

Simplifying
1 + 4i = 0

Solving
1 + 4i = 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 + 4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4i = 0 + -1
4i = 0 + -1

Combine like terms: 0 + -1 = -1
4i = -1

Divide each side by '4'.
i = -0.25

Simplifying
i = -0.25
Solution
i = {-0.25, -0.25}