(1+8i)(6+2i)=

Solution for (1+8i)(6+2i)= equation:

Simplifying
(1 + 8i)(6 + 2i) = 0

Multiply (1 + 8i) * (6 + 2i)
(1(6 + 2i) + 8i * (6 + 2i)) = 0
((6 * 1 + 2i * 1) + 8i * (6 + 2i)) = 0
((6 + 2i) + 8i * (6 + 2i)) = 0
(6 + 2i + (6 * 8i + 2i * 8i)) = 0
(6 + 2i + (48i + 16i2)) = 0

Combine like terms: 2i + 48i = 50i
(6 + 50i + 16i2) = 0

Solving
6 + 50i + 16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 25i + 8i2) = 0

Factor a trinomial.
2((3 + i)(1 + 8i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
Subproblem 2
Set the factor '(1 + 8i)' equal to zero and attempt to solve:

Simplifying
1 + 8i = 0

Solving
1 + 8i = 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 + 8i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8i = 0 + -1
8i = 0 + -1

Combine like terms: 0 + -1 = -1
8i = -1

Divide each side by '8'.
i = -0.125

Simplifying
i = -0.125
Solution
i = {-3, -0.125}