suppose fz u iv is analytic Under what circumstances will g

suppose f(z) =u + iv is analytic .Under what circumstances will g(z) =u -iv be analytic? HINT:Consider the functions f (z) +g(z) and f(z)-g(z).

Solution

Since f(z) is an Analytic Function , it implies that u is analytic and v is also analytic .

u = ( f(z) + g(z) ) / 2

and

v = ( f(z) - g(z) ) / 2i

are also Analytic function

Since , u and v are analytic , plus f(z) are also analytic . Therefore , g(z) should be analytic as well