(2+4i)(2+4i)=

Solution for (2+4i)(2+4i)= equation:

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

Multiply (2 + 4i) * (2 + 4i)
(2(2 + 4i) + 4i * (2 + 4i)) = 0
((2 * 2 + 4i * 2) + 4i * (2 + 4i)) = 0
((4 + 8i) + 4i * (2 + 4i)) = 0
(4 + 8i + (2 * 4i + 4i * 4i)) = 0
(4 + 8i + (8i + 16i2)) = 0

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

Solving
4 + 16i + 16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 4i + 4i2) = 0

Factor a trinomial.
4((1 + 2i)(1 + 2i)) = 0

Ignore the factor 4.
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 '(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
Solution
i = {-0.5, -0.5}