Question

please do do 1 a,b,c,d,e

and 2 a, b

Text exercise 26 Determine where each of the following funct (b) wz+5 Demonstrate that each of the following is harmonic and obtain 78 1 fails to be regular, bra) w = (2-4)(2+1) 2 conjugate function. u(x,y)= sinh x cos y u(x, y) = 4y(1 + 3x). (a) nb)

Answer 1

"Definition (regular function) ""A function of complex variables where each differentiable at each point in its domain is called regular function A regular function at a point is a function that is regular in some neighbourhood of that point "" (a) let W = z^3 + 4 here W is polynomial function we know that polynomial function is always differentiable at each point in C therefore W = z^3 + 4 is regular at each point in C therefore W = z^3 + 4 does not fails to be regular (b) let W = z/z + 5 here W is function of two polynomial function P(z) = z and q(z) = z + 5 here both p(z) and q(z) are regular at each point in C and q(z) = 0 for Z = -5 therefore W = z/z + 5 is regular at each point in C except z = -5"