Question

An analytic function whose real part is constant must itself be a constant

Answer 1

Answer:

Hint: use the Cauchy-Riemann equations, f(x,y)=g(x,y)+ih(x,y) if h(x,y) is constant, ∂xg=∂yh=0 and ∂yg=−∂xh=0 thus g is also constant. done.