Derivation of mapping for isometric rotation about i

[PcumP_Ravenclaw]

Homework Statement

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 ;

Homework Equations

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

The Attempt at a Solution

I have attached my attempt at the solution but my solution is wrong!

 

[Dick]

Homework Statement

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 ;

Homework Equations

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

The Attempt at a Solution

I have attached my attempt at the solution but my solution is wrong!

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.

 

[PcumP_Ravenclaw]

Thanks Dick!

I tried the problem and the solution is as attached

 

[Dick]

Thanks Dick!

I tried the problem and the solution is as attached

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 $f(z)=az+b$.