pset5 - Physics (PHZ) 3113 Mathematical Physics Florida...

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Unformatted text preview: Physics (PHZ) 3113 Mathematical Physics Florida Atlantic University Fall, 2010 Problem Set V Due: Tuesday, 5 October 2010 1. (Problems 2.9.12, 18 and 23, pp. 63–64) Express each of the following complex numbers in the Cartesian form z = x + i y . z (a) := 4e- 8 π i / 3 , z (b) := 1 + i 1- i 4 and z (c) := (1 + i) 48 ( √ 3- i) 25 . 2. (Problems 2.10.10, 19 and 23, pp. 66–67) Find all complex values of each of the following roots. z (a) := 5 √ 32 , z (b) := 3 √ i and z (c) := 4 q 8i √ 3- 8 . 3. (Problems 2.11.4, 7 and 10, p. 69) Find all complex values of each of the following functions. z (a) := e 3 ln2- i π , z (b) := tan(iln2) and z (c) := sin(ilni) . 4. (Problems 2.12.2, 3, 8, 12 and 16, p. 71) Verify each of the following identities using the definitions of the standard trigonometric and hyperbolic functions of a complex variable z = x + i y . a. cos z = cos x cosh y- isin x sinh y b. sinh z = sinh x cos y + icosh x sin y c. cosh2 z = cosh 2 z + sinh 2 z d. cos 4 z + sin...
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This note was uploaded on 10/21/2011 for the course PHZ 3113 taught by Professor Staff during the Fall '10 term at FAU.

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pset5 - Physics (PHZ) 3113 Mathematical Physics Florida...

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