Polchinski 2.4.1 change of coordinates

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I've been working through Polchinski on my own, and I have a really basic question. How would one derive equation 2.4.1? What does it even mean to write the stress tensor with the new indices z and z-bar? I thought this was obvious, but it isn't working out for me.
 
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clarification: this is not a homework problem, and it is not for a class.
 
got it. wow, forgot to lower indices. there is nothing deep here, as i had originally suspected.
 
Just did something analogous last week...dontcha just wish you would have waited??
 

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