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Tranformations from z to w plane

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Reply 20
Can anyone tell me how (simply) :

2i3iww=3\left|\frac{2i-3iw}{w}\right|=3

becomes


Unparseable latex formula:

|w-\frac{2}{3}|\right|=|w|

Reply 21
Original post by Charries
Can anyone tell me how (simply) :

2i3iww=3\left|\frac{2i-3iw}{w}\right|=3

becomes


Unparseable latex formula:

|w-\frac{2}{3}|\right|=|w|



2i3iww=3\left|\frac{2i-3iw}{w}\right|=3

Factor out the i.

i(23w)w=3\left|\frac{i(2-3w)}{w}\right|=3

Then since |ab|=|a| |b|

i23ww=3|i| \left|\frac{2-3w}{w}\right|=3

and since |i|=1

23ww=3 \left|\frac{2-3w}{w}\right|=3

factor out the three

3(2/3w)w=3 \left|\frac{3(2/3-w)}{w}\right|=3

32/3ww=3 |3| \left|\frac{2/3-w}{w}\right|=3

2/3ww=1 \left|\frac{2/3-w}{w}\right|=1

and since |a/b| = |a| / |b|

2/3ww=1 \frac{|2/3-w|}{|w|}=1

etc.
Reply 22
... and it was the etc bit I want to check.

Is |w-3| the same as |3-w|, because we take a take of -1 out, and

|-1| = |1| =1
Reply 23
Yes. | a - b | = | b - a |
Reply 24
Cheers
Reply 25
When I have :

x+iy=3\left|x+iy\right|=3

becomes

Unparseable latex formula:

\left x^2+y^2\right=9



So if I have

xiy=3\left|x-iy\right|=3

That's still the same circle isn't it?

If so, what's the right way to think about squaring this?

Unparseable latex formula:

\left x^2 + (-y)^2\right=9



or do I just forget about the minus sign when squaring, and do this :

Unparseable latex formula:

\left x^2 + y^2\right=9

Reply 26
Can anybody help me with my last post?

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