Question

prove that the transformation w=1/z takes circles on to circles
pls answer​

Answer 1

Answer:

you can use Google Chrome for the answer sorry for not responding the answer

Answer 2

Answer:

It follows that z−2=1/w−2, and the condition |z−2|=1 implies that

∣∣∣1w−2∣∣∣=1⟹|1−2w|=|w|

(at this point one may refer to Apollonius' theorem to see that this is equation of circle)

Now you may write w=u+iv to see that above is equivalent to

(1−2u)2+4v2=u2+v2⟹3u2+3v2−4u+1=0⟹u2+v2−43u+13=0

and last equation can be written as

(u−2/3)2+v2−19=0 which you should recognize as a circle.

Step-by-step explanation:

Mrk as brainelist

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