MAth P3 A2 help.....

[candy]

The complex number
2/-1 +i  is denoted by u.



(i) Find the modulus and argument of u and u^2. [6]



(ii) Sketch an Argand diagram showing the points representing the complex numbers u and u^2. Shade
the region whose points represent the complex numbers z which satisfy both the inequalities |z|<2
and |z-u^2| < |z-u|. [4]



please can someone answer part 2 for me!!! i dont understand!! 

its a question from may june 2007...i checked the markscheme but i don tunderstand it at all...can someone draw it n show it pllzzz...Thanks a lot!

[naffy]

IzI<2 is a circle at origin with radius 2

and then substitute the value of u and u^2 at both side.it should be a perpendicular bisector between both if i'm not mistaken

[louis]

Candy,
For l Z l <2, you have to draw a circle of radius 2. But the circumference line must be dotted and it means   the radius is not equal to 2 but less than 2.

From point U ( -1,-1) to U² (0, 2),join these two points. Draw a perpendicular bisector of this line
until it meets the circle at 2 points,namely  Z  and  Z1.
Finally, shade the area of the sector Z U2 Z1. Plz refer to the attachment.

 

[candy]

THANXXXXX ALOT louiss!!!  i really appreciate it!!!

[unfocused..]

any1 know where i cud get the may/june 2009 (paper 3)..?

[astarmathsandphysics]

Not yet.