Question

Find the domain of the function defined by f(z)=z/(z+z̅).

(a) Im(z)≠0

(b) Re(z)≠0

(c) Im(z)=0

(d) Re(z)=0

This question was addressed to me in unit test.

Origin of the question is Functions of a Complex Variable topic in chapter Complex Function Theory of Engineering Mathematics

Answer 1

Correct option is (b) Re(z)≠0

For explanation: Write z=x+iy ⇒ f(x+iy)=(x+iy)/(x+iy+x-iy)=(x+iy)/2x

=1/2+iy/2x ⇒ x≠0 ⇒ Re(z)≠0 .