# A2 complex number aaaaaaa....Watch

#1
I dont understand the transformations in complex numbers. So heres the question:
For the transformation
w=225/z z isnt equal zero

show that as z moves on the locus |z-25|=25, w lies on the locus |w-9|=|w| and identify its locus geometrically.

If u can solve this for me n give me some explanation I shall be very thankful to u.

I might not reply because i m gonna do some extra work on complex numbers.
So if u guys can quote me or PM me that will b very kind of u.
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9 years ago
#2
(Original post by windows?????)
So if u guys can quote me or PM me that will b very kind of u.
Here are some thoughts, on how I did it, although there may be a better way.

Re-arrange your definiton of "w" to get "z" in terms of "w", and then substitute into the equation for the locus of "z".

Use the fact that to get rid of the modulus signs (you'll probably need to get it all over a common denominator and make the denominator real before doing so) and then work through the algebra; it's messy.

I get it down to:

from which:

Although it's correct, I don't feel very happy with that last step, which makes me think there is a better way.
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9 years ago
#3
Can we not say
Spoiler:
Show

?
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9 years ago
#4
(Original post by rnd)
Can we not say
Spoiler:
Show

?
Just so much easier; and after all that torturous algebra I went through.
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#5
(Original post by ghostwalker)
Just so much easier; and after all that torturous algebra I went through.
thanx a lot for your help. Although I havnt reached that step of getting rid of mudulus but thnx any way for ur time.
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#6
(Original post by rnd)
Can we not say
Spoiler:
Show

?

Thnx a lot for ur help. I understand every step. thnx for ur time.
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#7
Hi.I got this question now:

The transformation
w=z+2/z+i
where z isnt equal -i,w isnt equal 1, maps the complex number z=x+iy onto the complex number w=u+iv.
(a)show that,if the point representing w lies on the real axis,the point representing z lies on the straight line.
(b)show further that, if the point representing w lies on the imaginary axis then the point representing z lies on the circle
|z+1+0.5i|=0.5√5
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9 years ago
#8
For part a) Write w in terms of x and y, make the denominator real, remember that w is real and by looking at the numerator deduce the relationship between x and y.

If you get part a you'll get part b too.
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#9
(Original post by rnd)
For part a) Write w in terms of x and y, make the denominator real, remember that w is real and by looking at the numerator deduce the relationship between x and y.

If you get part a you'll get part b too.
thnx
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#10
(Original post by rnd)
For part a) Write w in terms of x and y, make the denominator real, remember that w is real and by looking at the numerator deduce the relationship between x and y.

If you get part a you'll get part b too.
how do i make denominator real .can u show me please.thnx in advance.
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9 years ago
#11
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#12
(Original post by rnd)
oh yeah silly me.thnx
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