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Can someone help me find the point of discontinuity of a complex function? $$f(z)= \frac{2z-3}{z^2+2z+2}$$

Blue
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Halima Babangida
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1 Answers1

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Is it really a discontinuity point if the function is not even defined on it? For me, this "function" (you didn't specify the domain) is continuous.

hellofriends
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    he said it's a complex function, so presumably over C...

    that's just a guess though

     – O.S. Feb 19 '21 at 05:09
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    well, then he is hiding the values of the function on the poles. – hellofriends Feb 19 '21 at 05:10
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    hello @hellofriends, what do you "hiding the values $\cdots$?" – mjw Feb 19 '21 at 05:12
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    well if the function is defined in all the complex numbers. I'm assuming the roots of $z^2 + 2z + 2$ are complex numbers. So the function must be defined on these points. I'm not quite seeing which values the function takes on them, are you? – hellofriends Feb 19 '21 at 05:14
  • he wasn't hiding them. that was literally the question. where are the poles? – O.S. Feb 19 '21 at 05:18
  • Take a look at @NinadMunshi's hint to the question. Also, the poles are given in one of the answers. – mjw Feb 19 '21 at 05:20
  • @Reneo the question is what values that expression takes on it's singularities? I must have some eye disease then – hellofriends Feb 19 '21 at 05:22
  • not the values of the function at the singularities, but the values of z that produce singularities – O.S. Feb 19 '21 at 05:23
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    Sorry, that is not what the question asks. – hellofriends Feb 19 '21 at 05:23
  • @Reneo: The issue is this: https://math.stackexchange.com/questions/1087623/is-function-f-mathbb-c-0-rightarrow-mathbb-c-prescribed-by-z-rightarrow – Hans Lundmark Feb 19 '21 at 05:27