1. Find



since

as


2.
Which of the following limits does not exist?
Answer


limit of z5 Re(z)/Im(z) as z tends to 0


limit of z5 Re(z)/|z|5 as z tends to 0


limit of Im(z2)/Im(z) as z tends to 0


limit of Re(z2)/Im((1+i)z) as z tends to 0
The first one.

3. Which of the following sets is different from the others?
Answer


Image of Re(z)>1/2 under f(z)= 1/z - 1


{z | |z100|<|z2| }


Preimage of {w| Re(w)<1} under f(z)=|z|


{z| |conjugate(z)|<1 and Re(1/(1+z))>0}
the second one