Problem on complex derivative

Hi,

here is a problm on complex derivative. I will be appreciated if you
give me some help.

Given W and S complex vectors, and b and g compelx scalars, the
following partial derivative with respect to conjugat of W, W*

d/(dW*) ( Re [ b* (W^H S - g) ] ) = b* S, (note, H, hermittian
transpose)

why not Re(b* S)?

Suppose b = br + j bi, S = Sr + j Si,

d/(dW*) ( Re [ b* (W^H S - g) ] )
= d/(dW*) ( [ br Re(W^H S - g) + bi Im(W^H S - g) ] )
= d/(dW*) ( br Re(W^H S - g) ) + d/(dW*) ( bi Im(W^H S - g) )
= br d/(dW*) Re(W^H S - g) + bi d/(dW*) ( Im(W^H S - g) )
= br Re ( d/(dW*) (W^H S - g)) + bi Im( d/(dW*) (W^H S - g) )
= br Re(S) + bi Im(S) = Re(b* S)

I am not sure if Re ( d/(dW*) (W^H S - g)) = Re(S) or S, please help.

Thanks.

Lin. S.

.

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