Hello!!!

I thought of giving you the subjects of mathematics that I gave examinations in order to enter in the university!!I am waiting your opinion about them!!!

1st Exercise:

It is given that the fantastic number z1=(1+i√3)/2 it is root of equation z²+z•b+c=0 ,where b and c real numbers.

a.Prove that b=-1 and c=1.

b.Prove that z1³=-1.

c.Find the geometric place of pictures of fantastic number w, for which it is in effect:

|w|=|z1-z1*|

look!!!!In 1.c the 2nd z1* is complex conjugate.

This is the 1st exercise and of course easier relatively with the other exercises.I will try to post and the other two exercises if you want...

Sorry for my english errors because I translate from greek!!

Thanks for your time!!!