Help with a complex mapping

  • Thread starter Stephen88
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  • #1
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Homework Statement



Let the Complex mapping
z → f(z) =(1 + z)/(1 − z)
1.What are the images of i and 1 − i and 2.What are the images of the real and the imaginary axes?




The Attempt at a Solution


For i we have f(i)=(1+i)/(1-i) since i(depending on the power) can be i,-i,1,-1=>0, (1+i)/(1-i),(1-i)/(1+i)
For 1 − i we have 1,-3,(2-i)/i,(2+i)/i.
Not sure about the second part..
 

Answers and Replies

  • #2
vela
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Homework Statement



Let the Complex mapping
z → f(z) =(1 + z)/(1 − z)
1.What are the images of i and 1 − i and 2.What are the images of the real and the imaginary axes?




The Attempt at a Solution


For i we have f(i)=(1+i)/(1-i) since i(depending on the power) can be i,-i,1,-1=>0, (1+i)/(1-i),(1-i)/(1+i)
I'm not sure why you're looking at the various powers of i. It only appears to the first power in your expression. Use the following method to simplify it:
$$f(i) = \frac{1+i}{1-i} = \frac{1+i}{1-i}\cdot\frac{1+i}{1+i} = \ ?$$
 
  • #3
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Sorry I was tired,thanks for the reply..how should I think about the both parts of the problem.?..Also.I"m getting -1 for f(i)
 
  • #4
vela
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That's still wrong. You should find f(i)=i.

If z=x+iy is a point on the imaginary axis, you know that x=0, so you want to find f(z)=f(iy). Can you take it from there?
 

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