I am stuck on this real complex question- i have done the first 3 parts but m stuck on the last- can't figure out the right shaded portion.
The complex number -2+i is denoted by u.
a) Given that u is a root of the equation x^3-11x-k=0, where k is real, find the value of k.
b) Write down the other complex root of this equation.
c) Find the modulus and argument of u.
d) Sketch an Argand diagram showing the point representing u. Shade the region whose points represent the complex numbers z satisfying both the inequalities
|z|<|z-2| and 0<arg(z-u)<π/4
So far i have reached 3 inequalities
1) y<x+3, 2)y<1 and 3) x<1
Can somebody please help me with this question. If i am doing anything wrong plz correct me.