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**1. The problem statement, all variables and given/known data**

a)For a general operator A, show that and i(A-A

^{+}) are hermitian?

b) If operators A and B are hermitian, show that the operator (A+B)^n is Hermitian.

**2. Relevant equations**

**3. The attempt at a solution**

The first part I did,

(A+A

^{+})

^{+}=(A

^{+}+A)=(A+A

^{+})

i(A-A

^{+})=[i(A-A

^{+})]

^{+}=(iA)

^{+}-(iA

^{+})

^{+})=i(A-A

^{+})

The second part I used binomial expansion (induction) but I was told they do not commute so this cannot be done?

Is my answer to the first part correct and what route should I take for the second? Thanks