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HW 1 Solutions

The document summarizes the key steps and solutions to 3 problems from homework 1. Problem 1 involves solving various equations and expressions. Problem 2 involves evaluating trigonometric functions of logarithms. Problem 3 discusses determining whether functions are analytic and provides examples of harmonic and analytic functions.

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nick10686
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70 views2 pages

HW 1 Solutions

The document summarizes the key steps and solutions to 3 problems from homework 1. Problem 1 involves solving various equations and expressions. Problem 2 involves evaluating trigonometric functions of logarithms. Problem 3 discusses determining whether functions are analytic and provides examples of harmonic and analytic functions.

Uploaded by

nick10686
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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HW 1 Key

Problem 1:
A) i)  484 
 ii) 23‐2i 
 iii)   
 iv)    
  v)   

      B)   i) | 2|= | 4| x = ‐1 

 ii)  

iii) 

iv)  
 

c) 

 
Problem 2: 
  A. i) ln√2 + i  
 ii) ‐  

 iii) 1 

  iv) cos (ln3)+ i sin (ln3) 

 C.    

cos 4 6  

sin 4 4 sin cos  

Problem 3: 
 B.  Not Analytic  
 C.  f(z) = (x3 – 3xy2‐d) + i(3x2y – y3 + c) 

 D. u(x,y) is harmonic 

  f(z) = (cos x cosh y) – i(sinx sinh y + c) 

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