(6+8i)(6+8i)=0

Solution for (6+8i)(6+8i)=0 equation:

Simplifying
(6 + 8i)(6 + 8i) = 0

Multiply (6 + 8i) * (6 + 8i)
(6(6 + 8i) + 8i * (6 + 8i)) = 0
((6 * 6 + 8i * 6) + 8i * (6 + 8i)) = 0
((36 + 48i) + 8i * (6 + 8i)) = 0
(36 + 48i + (6 * 8i + 8i * 8i)) = 0
(36 + 48i + (48i + 64i2)) = 0

Combine like terms: 48i + 48i = 96i
(36 + 96i + 64i2) = 0

Solving
36 + 96i + 64i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 24i + 16i2) = 0

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

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

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Solution
i = {-0.75, -0.75}