(4-2i)(1-2i)=

Solution for (4-2i)(1-2i)= equation:

Simplifying
(4 + -2i)(1 + -2i) = 0

Multiply (4 + -2i) * (1 + -2i)
(4(1 + -2i) + -2i * (1 + -2i)) = 0
((1 * 4 + -2i * 4) + -2i * (1 + -2i)) = 0
((4 + -8i) + -2i * (1 + -2i)) = 0
(4 + -8i + (1 * -2i + -2i * -2i)) = 0
(4 + -8i + (-2i + 4i2)) = 0

Combine like terms: -8i + -2i = -10i
(4 + -10i + 4i2) = 0

Solving
4 + -10i + 4i2 = 0

Solving for variable 'i'.

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

Factor a trinomial.
2((1 + -2i)(2 + -1i)) = 0

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

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Subproblem 2
Set the factor '(2 + -1i)' equal to zero and attempt to solve:

Simplifying
2 + -1i = 0

Solving
2 + -1i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Solution
i = {0.5, 2}