3) (10 pts) For f(2)= a) Find the real part (0) b) Find the imaginary part...
(10 ptsFor f(3) = 3+1 a) Find the real part (u) b) Find the imaginary part (v) c) Use u and v to evaluate f(2)atz = 9 - 6
1. if the real part of an analytic function, f(z), is given find the imaginary part, v(x, y) and f(z) as a function of x. (step by step) 2. Evaluate the following complex integral (step by step) 1. If the real part of an analytic function, f(z), is given as 2 - 12 (x2 + y2)2 find the imaginary part, v(x,y), and f(z) as a function of z. 2. Evaluate the following complex integral:
Problem 2. (15 points) a) Find the real part u(x,y) and imaginary part v(x,y) of f(z) = (1+2i)z+ (i – 1)2 +3 b) Verify if the above function is analytic c) Using Laplace's equation verify if the real part u(x,y) is harmonic.
a) Find the real part u(x,y) and imaginary part v(x,y) of f(2)= (1+2i )z? + (i – 1)2 +3 b) Verify if the above function is analytic c) Using Laplace's equation verify if the real part u(x,y) is harmonic.
Questions. (20 pts.) a) Find the real part and imaginary part of the following complex numbers 1. jel- 2. (1 - 0260 3. b) Find polar form of the following numbers 31-3 9 Question 2. (20 pts.) a) Simplify (2< (5/7) (2<(")) 2 < (-1/6) b) Solve z+ + Z2 + 1 = 0
Need help for part(b) thx :) Question 1: Find the real and imaginary parts, u and y, and the natural domain of (a) f(2)=z + (6) 9(2) = cc-*
(10 pts) Calculate the following a) Find the real and imaginary parts of e 3+nj b) Find the real and imaginary parts of ez? c) Write in polar form: 1+j
1 Find the real part of (a+b2T a 6, b=10. 5 pts Question 2 What is the imaginary part of where n 102. Question 3 5 pts Consider the following complex-valued function of of a real-variable w 1 f (w)= 1+aexp(-ju) where a 0.3. Find the phase of f (7).
find the real and imaginary part(u and v) of the complex function lnz a) Find the real and imaginary parts (u and v) of the complex functions: - CZ Find out whether the functions in (a) satisfy the Cauchy-Riemann equations.
I 5) (10 pts) Calculate the following a) Find the real and imaginary parts of e8**) b) Find the real and imaginary parts of c) Write in polar form: 1+1