Homework+2

1. Find math \lim\limits_{z\to 2i} \frac{z^2-4iz-4}{\overline z + 2i} math

math \lim\limits_{z\to 2i} \frac{z^2-4iz-4}{\overline z + 2i}= \lim\limits_{z\to 2i} \frac{(z-2i)^2}{\overline {z - 2i}}= \lim\limits_{w\to 0} \frac{w^2}{\overline w}=0 math since math math as math w\to 0 math
 * \frac {w^2}{\overline w}|=|w|\to 0

2. Which of the following limits does not exist? Answer The first one.
 * < ||<  ||<  limit of z 5 Re(z)/Im(z) as z tends to 0  ||
 * < ||<  ||<  limit of z 5 Re(z)/|z| 5 as z tends to 0  ||
 * < ||<  ||<  limit of Im(z 2 )/Im(z) as z tends to 0  ||
 * < ||<  ||<  limit of Re(z 2 )/Im((1+i)z) as z tends to 0  ||

3. Which of the following sets is different from the others? Answer the second one
 * < ||<  ||<  Image of Re(z)>1/2 under f(z)= 1/z - 1  ||
 * < ||<  ||<  {z | |z 100 |<|z 2 | }  ||
 * < ||<  ||<  Preimage of {w| Re(w)<1} under f(z)=|z|  ||
 * < ||<  ||<  {z| |conjugate(z)|<1 and Re(1/(1+z))>0}  ||