Question for S08 Maths Paper 3

[twinklebell.star]

i cant understand what was the question, s08 Maths Paper 3 Question 5.
how can i approach it?

5. The variable complex number Z is given by
z=2cos x + i(1-2sinx)
where x takes all values in the interval -Л < x ≤ Л
(1) show that |z-i|=2, for all values of x. Hence sketch, in an Argand diagram, the locus of the point representing z.
(2) prove that the real part of 1/(z+2-i)
is constant for -Л < x < Л

 

[weesha]

in first part.. u actually have to identify the modulus of z-i
for that, open the brackets and shift i to l.h.s
take out 2 as common
z-i=2[cosx - i(sinx)]
it is the general form where 2 is the mod
it is proven.... then draw the circle of radius 2 and centre i