A2 complex number aaaaaaa.... Watch

windows?????
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#1
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I dont understand the transformations in complex numbers.:mad: 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.:confused:

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

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.
Thanx in advance
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ghostwalker
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#2
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(Original post by windows?????)
So if u guys can quote me or PM me that will b very kind of u.
Thanx in advance
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 |z|^2=z\bar{z} 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:

9-w=\bar{w}

from which:

|w-9|=|w|


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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rnd
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Can we not say
Spoiler:
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z=\frac{225}{w}

|z-25|=25

\left|\frac{225}{w}-25\right|=25

\left|\frac{225-25w}{w}\right|=25

\frac{|225-25w|}{|w|}=25

|225-25w|=25|w|

|25(9-w)|=25|w|

25|9-w|=25|w|

|9-w|=|w|

?
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ghostwalker
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(Original post by rnd)
Can we not say
Spoiler:
Show

z=\frac{225}{w}

|z-25|=25

\left|\frac{225}{w}-25\right|=25

\left|\frac{225-25w}{w}\right|=25

\frac{|225-25w|}{|w|}=25

|225-25w|=25|w|

|25(9-w)|=25|w|

25|9-w|=25|w|

|9-w|=|w|

?
Just so much easier; and after all that torturous algebra I went through.
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windows?????
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(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:woo: but thnx any way for ur time.
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windows?????
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(Original post by rnd)
Can we not say
Spoiler:
Show

z=\frac{225}{w}

|z-25|=25

\left|\frac{225}{w}-25\right|=25

\left|\frac{225-25w}{w}\right|=25

\frac{|225-25w|}{|w|}=25

|225-25w|=25|w|

|25(9-w)|=25|w|

25|9-w|=25|w|

|9-w|=|w|

?

Thnx a lot for ur help. I understand every step. thnx for ur time.
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windows?????
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#7
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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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rnd
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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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windows?????
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(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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windows?????
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#10
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(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:woo: .can u show me please.thnx in advance.
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rnd
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#11
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\frac{a+bi}{c+di}=\frac{(a+bi)(c-di)}{(c+di)(c-di)}=...
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windows?????
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#12
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(Original post by rnd)
\frac{a+bi}{c+di}=\frac{(a+bi)(c-di)}{(c+di)(c-di)}=...
oh yeah silly me.thnx
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