- #1

- 45

- 0

## Homework Statement

To show [J

^{2}, J

_{+}] = 0

2. Homework Equations

2. Homework Equations

J

_{+}= J

_{x}+

*i*J

_{y}

[J

^{2}, J

_{x}] = 0

[J

^{2}, J

_{y}] = 0

## The Attempt at a Solution

Step 1: L.H.S. = [J

^{2}, J

_{+}]

Step 2: L.H.S. = [J

^{2}, J

_{x}+

*i*J

_{y}]

Step 3: L.H.S. = [J

^{2}, J

_{x}] +

*i*[J

^{2}, J

_{y}]

Step 4: L.H.S. = 0 + 0

Step 5: L.H.S. = 0

L.H.S. = R.H.S.

I'm kinda confuse about 'Step 3'. Can we take out the '

*i*' from whole bracket? If yes, then do I have to give any reason for it?