Hi guys. I was hoping you could help me find the limit of a complex function. So here goes:
The lim z --> i of [i(z)^3 - 1 ] / (z+i)
The Attempt at a Solution
If z approaches i, then (x,y) approaches (0,1)
Do I let z = x+iy, then expand out the cube and plug in 0's for x's and 1's for y's in one limit?
Or do I do two limits, one letting x go to 0, the other letting y go to one and compare these two limits?
Or do I just plug in i for z right off the bat and expand that out?
Basically, how is it possible to test the limit from every approach in the complex plane without doing some
kind of epsilon / delta proof.
Thank you very much if you respond.