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##.