Unformatted text preview: f ( z ). (Hint: Use your answer from problem #2.) 6. Using the Cauchy-Riemann equations, show that f ( z ) = 1 /z is holomorphic on its domain and that its derivative is-1 /z 2 . (Hint: The real and imaginary parts of 1 /z were given in lecture.) 7. Show that d dz sin z = cos z . (Hint: Write sin z in terms of the exponential function and then use the rules for diﬀerentiation and the fact that we know how to diﬀerentiate exponential functions.) 8. Let f ( z ) = ze πz . Compute f ( i ). 1...
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This note was uploaded on 07/25/2008 for the course MATH V1202 taught by Professor Neel during the Spring '07 term at Columbia.
- Spring '07