Solve SU(2) Parametrization Problem w/ Westra's PDF

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The discussion centers on the SU(2) parametrization problem as presented in Westra's PDF. The key point raised is whether assuming b = 0 reduces the generality of the parametrization. The conclusion is that while assuming b = 0 may seem limiting, it allows for a distinct strategy that does not rely on division by b, thus maintaining the integrity of the problem-solving approach.

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yoreh
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I have a trivial mathematical problem with SU(2) parametrization. In www.mat.univie.ac.at/~westra/so3su2.pdf , section 3, there is a sentence starting with "We first assume b = 0 and find then(...)". My question is: doesn't assuming that b = 0 reduce generality of our parametrization? If not, why?
 
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What you need to do there is to consider two mutually exclusive possibilities separately. If b≠0, you can use a strategy that involves division by b. If b=0, that strategy doesn't work, but you can finish the problem without it.
 
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