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Yet Another Question on the Complex Square Root Function ... Palka, Example 1.5, Chapter III

Peter

Well-known member
MHB Site Helper
Jun 22, 2012
2,891
I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ...

I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ...

I have yet another question regarding Example 1.5, Section 1.2, Chapter III ...

Example 1.5, Section 1.2, Chapter III, reads as follows:




Palka - 1 - Example 1.5, Section III - PART 1 ... .png
Palka - 2 - Example 1.5, Section III - PART 2 ... .png




About half way through the above example from Palka we read the following:

" ... ... Since \(\displaystyle \mid 1/ \sqrt{z} \mid \ = 1/ \sqrt{ \mid z \mid } \to \infty\) as \(\displaystyle z \to 0\) ... ... "



Can someone please explain exactly how/why \(\displaystyle \ \mid 1/ \sqrt{z} \mid \ = 1/ \sqrt{ \mid z \mid }\) ...


Help will be appreciated ...

Peter
 
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