Re: Difficulties in chapter 5

Just bought RTR and just discovered this forum, so apologies for delay!

Had to comment on this topic:

vasco is correct, but to me the point is that when Penrose gives this expression for z (ie logw) the expression

cannot be directly derived based on what he has said so far in the book. In fact, vasco's explanation/derivation is given by Penrose in a different form on the next page (p95 in my copy) after the para starting with "We can best understand...".

The closest Penrose gives to a justification for this expression is that when we multiply complex numbers we multiply the moduli and add the arguments. In fact in note [5.4] he admits that, from what has been given to us at this point in the book, an expression such as

also has the required properties for

but the real factor of 5 I have used here would be wrong -- and he says that to prove that (ie that the imaginary part should not be a real multiple of

you need calculus.

To summarize: the expression near the top of p94 is correct, and I

know it is correct based on the mathematics I did at school, but it seems to me that it cannot be directly derived from what Penrose has said by that point in the book. Do I have that right?