Derivation of mapping for isometric rotation about i

1. Nov 15, 2014

PcumP_Ravenclaw

1. The problem statement, all variables and given/known data
2. Find the formulae as in (3.4.1) for each of the following:
(a) the rotation of angle π/2 about the point i ;

2. Relevant equations
The equation 3.4.1 is given below.
$f(z) → z*a + b$
where a, b and z are all complex numbers

3. The attempt at a solution
I have attached my attempt at the solution but my solution is wrong!!

Attached Files:

• Untitled1.jpg
File size:
29.3 KB
Views:
75
2. Nov 15, 2014

Dick

You want to start out with $\left( z-w \right) e^{i \theta}$. No absolute value! Now just put in what $w$ and $\theta$ are.

3. Nov 16, 2014

PcumP_Ravenclaw

Thanks Dick!!

I tried the problem and the solution is as attached

Attached Files:

• Untitled2.jpg
File size:
23.2 KB
Views:
68
4. Nov 16, 2014

Dick

I'm not sure what part of that is supposed to be the answer. The answer is $f(z)=\left( z-w \right) e^{i \theta}+w$. You seem to know $w=i$ and $e^{i \pi/2}=i$. Just put those values in! Then try to express it in the form $f(z)=az+b$.

Last edited: Nov 16, 2014