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# FP2 Complex numbers Exercise 3H Q15 watch

1. Hey guys I need help with Edexcel FP2 exercise 3H question 15

can some one please go through it with me , thanks in advance
question:
the transformation T from the z-plane, where z=x+iy, to the w-plane where w = u + iv, is given by : w = z + 4/z

show that the transformation T maps the points on a circle with modulus 2 (mod(z)=2 i.e centre 0,0 ) to the points in the interval [-k,k] on the real axis, state the value of the constant k.
2. Write z in polar form using |z|=2 then sub into the transformation.
3. (Original post by james22)
Write z in polar form using |z|=2 then sub into the transformation.
I did ( |z|=2 came with the question) but im not sure how to sub it in
4. (Original post by nmanvi)
I did ( |z|=2 came with the question) but im not sure how to sub it in
What is the general form of a complex number in polar form?
5. (Original post by james22)
What is the general form of a complex number in polar form?
I am not sure I havent done any polar coordinates, in the middle of complex numbers
6. (Original post by nmanvi)
I am not sure I havent done any polar coordinates, in the middle of complex numbers
Have you seen things like or ?
7. (Original post by james22)
Have you seen things like or ?
yeppp, will they help me answer the question?
8. (Original post by nmanvi)
yeppp, will they help me answer the question?
Yes, you should know that any complex number can be written in the form where r is the modulus of z.

EDIT: You also need that cos(x)+isin(x)=e^ix.

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