First off, sorry if this is in the wrong section it could be in calculus I guess, but my unit is titled complex analysis so I thought it might go in here.

So I have just started Complex analysis for the first time and just needed some help.

When I am required to find all the points in the complex plane at which a complex function of several variables (i.e f(x+iy)=u(x,y)+iv(x,y)) is differentiable, what steps do i take in determining the answer. When dealing with real numbers i would usually find the answer via inspection or asymptotes ect. But i am having trouble picturing it on the complex plane. Do i use the Cauchy-Riemann Equations to test for analyticity?

For example f(x+iy)= 2(x^2-y^2) -i4xy , has the answer differentiable at z=0. but how do i determine this.

Any help would be greatfully appreciated

as my lecturer has not covered this yet but trying to wrap my head around it