What is the correct position of u on an Argand diagram?

[ishterz]

Hello.I have done all the parts and just have problems with the last one. I've pasted the whole question though to include all the details which may be needed

Homework Statement

The complex number −2 + i is denoted by u.
(i) Given that u is a root of the equation x3 − 11x − k = 0, where k is real, find the value of k. [3]
(ii) Write down the other complex root of this equation. [1]
(iii) Find the modulus and argument of u. [2]
(iv) Sketch an Argand diagram showing the point representing u. Shade the region whose points
represent the complex numbers ß satisfying both the inequalities
|ß| < |ß − 2| and 0 < arg(ß − u) < pi/4 (45 degrees)

The Attempt at a Solution

I got k = 20
b) -2-i
(iii) 5^1/2 (cos153.4 + isin153.4)

(iv) I solved it by doing:

x^2 +y^2 = x^2 +y^2 -4x + 2y +5
y= 2x - 5/2

I don't know if I'm right because the mark scheme says :
iv) Show point representing u in relatively correct position in an Argand diagram B1
Show vertical line through z = 1 B1
Show the correct half-lines from u of gradient zero and 1 B1
Shade the relevant region

??

PLease help!
Thanks :)

 

[tiny-tim]

hello ishterz!

(have a pi: π and try using the X² icon just above the Reply box )

|ß| < |ß − 2| and 0 < arg(ß − u) < pi/4 (45 degrees)
…
x^2 +y^2 = x^2 +y^2 -4x + 2y +5

erm …

you've used |ß - 2 - i| instead of |ß| ​

(btw, there is a simpler method, just using elementary geometry)