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# Complex analysis- limits help please watch

1. Can some1 explain this to me please?

For the first one I'm not understanding why they've taken the modulus and how mod(z) is related to (z bar)^2/(z)?
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2. ^^^
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3. (Original post by e^x)
^^^
Sorry, but what is the question? Are you asking why ?
4. (Original post by e^x)
Can some1 explain this to me please?

For the first one I'm not understanding why they've taken the modulus and how mod(z) is related to (z bar)^2/(z)?
For a complex limit to exist, the limit must have the same value, regardless of by which path in the complex plane. Here we have:

If , how does that distinguish those two cases, and why does one of them fail to have a limit?
5. (Original post by atsruser)
For a complex limit to exist, the limit must have the same value, regardless of by which path in the complex plane. Here we have:

If , how does that distinguish those two cases, and why does one of them fail to have a limit?

For the first case z-->0 is the same as saying r-->0 so the first one has a limit of 0.

I'm still confused for the second case?
6. (Original post by e^x)
For the first case z-->0 is the same as saying r-->0 so the first one has a limit of 0.
Yes. Can you show this more formally? (Hint: Squeeze/Sandwich theorem)

I'm still confused for the second case?
As you noted but can be chosen so that along any radial line. For the limit to exist, the expression must approach the same limiting value regardless of which by radial line . The specific radial line is determined by .

Can you find two different which give different limits?

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