These questions made me almost quit maths. Whew, they are tough!

1. Determine the characteristics given pointsz=-1/, where ||=2 of the shape that is formed.

2. A curve formed by iz3+z2-z+i=0 encloses area A. Find the area?

3. Area Z is bounded by arg|z|/4 and |z-1|<|z-3|, determine the area.

4. A circle of radius 1 has z lying in it and z1. Solve for the locus z/(1-z2).

5. How can you describe region X which is given by|z-i|z||-|z+i|z||=0.

6. Region X which has its area as 2, is determined by zz+a(z+z)+a=0. What will be the area of a region zz+2a(z+z)+a=0 assuming that a2-7a+10=0?

7. Sets S1={zC: |z|<4}, S2={zC:Im[(z-1+3i)/(1-3i)]>0} and S3={zC: Re z>0} share a common region. Determine the area of this region.

8. Function Q is defined by f(z)=z/(z+z). What is its domain?

9. Determine in polar form the function f(z)=z+1/z.

10.Assuming is the cube root of unity and Im()>0, determine the value of |f()|+Arg f() in the function f(z)=zi.