# show harmonic by representing by composition of maps

• February 10th 2009, 11:34 PM
szpengchao
show harmonic by representing by composition of maps
show $tan^{-1}(\frac{2x}{x^{2}+y^{2}-1})$ is harmonic by considering $h(w(z))=log(\frac{i+z}{i-z})$

i found that h(w(z)) is just the same as the function required. but how can i show it is harmonic by writing it as composition of maps?
• February 11th 2009, 02:50 PM
ThePerfectHacker
Quote:

Originally Posted by szpengchao
show $tan^{-1}(\frac{2x}{x^{2}+y^{2}-1})$ is harmonic by considering $h(w(z))=log(\frac{i+z}{i-z})$

i found that h(w(z)) is just the same as the function required. but how can i show it is harmonic by writing it as composition of maps?

Remember that the real and imaginary parts of an analytic function on an open set S are harmonic on S.