# Help with a complex mapping

1. Feb 5, 2012

### Stephen88

1. The problem statement, all variables and given/known data

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?

3. 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..

2. Feb 6, 2012

### vela

Staff Emeritus
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. Feb 6, 2012

### Stephen88

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. Feb 6, 2012

### vela

Staff Emeritus
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?