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Unformatted text preview: ( z ) =i log ( z + i (1z 2 ) 1 / 2 ) . Explain how to introduce cuts to give a branch with cos1 (0) = / 2. 4. (20 pts.) Show that tan1 ( z ) = i 2 log i + z iz and tanh1 ( z ) = 1 2 log 1 + z 1z . 5. (10 pts.) Determine all values of i i and log ((1 + i ) i ) and plot them in the complex plane. 6. (25 pts.) Determine the branch points of the function p ( z1)( z6)( z + 2) . Construct cuts and dene a branch so that z = 4 does not lie on a cut, and such that w = 6 i when z = 4. Due at 5pm on Wed. October 14....
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 Fall '09
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