(6+8j)*(6+8j)=100

Solution for (6+8j)*(6+8j)=100 equation:

Simplifying
(6 + 8j)(6 + 8j) = 100

Multiply (6 + 8j) * (6 + 8j)
(6(6 + 8j) + 8j * (6 + 8j)) = 100
((6 * 6 + 8j * 6) + 8j * (6 + 8j)) = 100
((36 + 48j) + 8j * (6 + 8j)) = 100
(36 + 48j + (6 * 8j + 8j * 8j)) = 100
(36 + 48j + (48j + 64j2)) = 100

Combine like terms: 48j + 48j = 96j
(36 + 96j + 64j2) = 100

Solving
36 + 96j + 64j2 = 100

Solving for variable 'j'.

Reorder the terms:
36 + -100 + 96j + 64j2 = 100 + -100

Combine like terms: 36 + -100 = -64
-64 + 96j + 64j2 = 100 + -100

Combine like terms: 100 + -100 = 0
-64 + 96j + 64j2 = 0

Factor out the Greatest Common Factor (GCF), '32'.
32(-2 + 3j + 2j2) = 0

Factor a trinomial.
32((-2 + -1j)(1 + -2j)) = 0

Ignore the factor 32.
Subproblem 1
Set the factor '(-2 + -1j)' equal to zero and attempt to solve:

Simplifying
-2 + -1j = 0

Solving
-2 + -1j = 0

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

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

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

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

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

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

Simplifying
1 + -2j = 0

Solving
1 + -2j = 0

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

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

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

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

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

Simplifying
j = 0.5
Solution
j = {-2, 0.5}