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prob04 - e z = z if and only if-π< Im z< π 4 Find the...

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Problem Set 4 Due February 26 th , 2007 1. Write the function f ( z ) = 100 k =0 e kz as the ratio of two sines. 2. Verify the identity sin z - sin w = 2 cos ( z + w 2 ) sin ( z - w 2 ) , and show that sin z = sin w if and only if z = w + 2 or z = - w + (2 k + 1) π, where k is an integer. 3. Prove that Log
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Unformatted text preview: e z = z if and only if-π < Im z < π . 4. Find the derivative of the principal branch of z 1+ i at z = i . 5. Show that cos-1 z =-i log ( z + ( z 2-1) 1 / 2 ) . 6. p.129 1, 2....
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