Need help for part(b) thx :) Question 1: Find the real and imaginary parts, u and...
(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
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.
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.
3) (10 pts) For f(2)= a) Find the real part (0) b) Find the imaginary part (V) c) Use u and v to evaluate f (x)at z = 9 - 61
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:
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.
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
could use some help on these, will rate! Find the real and imaginary parts of (2ei)' b) z= (2+3i)3 Problem 1.29 a) z= Problem 1.25 Light from a helium-neon laser has a wavelength of 633 nm and a wave speed of 3.00 x 10 m/s. Find the frequency, period, angular frequency, and wave number for this light.
Show that the real and imaginary parts of the complex-valued function f(x) = cot z are - sin 2.c sinh 2g u(I,y) v(x,y) = cos 2x - cosh 2y cos 2x - cosh 2y (cot 2 = 1/tan 2)
Problem 8. Let f(z) = u(x, y) iv(x, y) be an entire function with real and imaginary parts u(x, y) and v(x, y). Assume that the imaginary part is bounded v(x, y) < M for every z = x+ iy. Prove that f is a constant 1