2j-j^2=1

Solution for 2j-j^2=1 equation:

Simplifying
2j + -1j2 = 1

Solving
2j + -1j2 = 1

Solving for variable 'j'.

Reorder the terms:
-1 + 2j + -1j2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2j + -1j2 = 0

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

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

Simplifying
-1 + j = 0

Solving
-1 + j = 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 + j = 0 + 1

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

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

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

Simplifying
1 + -1j = 0

Solving
1 + -1j = 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 + -1j = 0 + -1

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

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

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

Simplifying
j = 1
Solution
j = {1, 1}