10-5i(10-5i)=

Solution for 10-5i(10-5i)= equation:

Simplifying
10 + -5i(10 + -5i) = 0
10 + (10 * -5i + -5i * -5i) = 0
10 + (-50i + 25i2) = 0

Solving
10 + -50i + 25i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -10i + 5i2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + -10i + 5i2)' equal to zero and attempt to solve:

Simplifying
2 + -10i + 5i2 = 0

Solving
2 + -10i + 5i2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.4 + -2i + i2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2i + -0.4 + i2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2i + i2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2i + i2 = 0 + -0.4
-2i + i2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2i + i2 = -0.4

The i term is -2i.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2i + 1 + i2 = -0.4 + 1

Reorder the terms:
1 + -2i + i2 = -0.4 + 1

Combine like terms: -0.4 + 1 = 0.6
1 + -2i + i2 = 0.6

Factor a perfect square on the left side:
(i + -1)(i + -1) = 0.6

Calculate the square root of the right side: 0.774596669

Break this problem into two subproblems by setting 
(i + -1) equal to 0.774596669 and -0.774596669.

Subproblem 1
i + -1 = 0.774596669

Simplifying
i + -1 = 0.774596669

Reorder the terms:
-1 + i = 0.774596669

Solving
-1 + i = 0.774596669

Solving for variable 'i'.

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 = 0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + i = 0.774596669 + 1
i = 0.774596669 + 1

Combine like terms: 0.774596669 + 1 = 1.774596669
i = 1.774596669

Simplifying
i = 1.774596669

Subproblem 2
i + -1 = -0.774596669

Simplifying
i + -1 = -0.774596669

Reorder the terms:
-1 + i = -0.774596669

Solving
-1 + i = -0.774596669

Solving for variable 'i'.

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 = -0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + i = -0.774596669 + 1
i = -0.774596669 + 1

Combine like terms: -0.774596669 + 1 = 0.225403331
i = 0.225403331

Simplifying
i = 0.225403331

Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {1.774596669, 0.225403331}
Solution
i = {1.774596669, 0.225403331}