(6-2i)(6-2i)=0

Solution for (6-2i)(6-2i)=0 equation:

Simplifying
(6 + -2i)(6 + -2i) = 0

Multiply (6 + -2i) * (6 + -2i)
(6(6 + -2i) + -2i * (6 + -2i)) = 0
((6 * 6 + -2i * 6) + -2i * (6 + -2i)) = 0
((36 + -12i) + -2i * (6 + -2i)) = 0
(36 + -12i + (6 * -2i + -2i * -2i)) = 0
(36 + -12i + (-12i + 4i2)) = 0

Combine like terms: -12i + -12i = -24i
(36 + -24i + 4i2) = 0

Solving
36 + -24i + 4i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -6i + i2) = 0

Factor a trinomial.
4((3 + -1i)(3 + -1i)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Subproblem 2
Set the factor '(3 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Solution
i = {3, 3}