- #1
jjr
- 51
- 1
Homework Statement
Calculate the following limit if it exists
## lim_{z\to -1}\frac{\sqrt{z}-i+\sqrt{z+1}}{\sqrt{z^2-1}} ##
the branch of root is chosen to that ##\sqrt{-1}=i##
Homework Equations
3. The Attempt at a Solution
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By inserting ##z=-1## directly, I get a ##\frac{0}{0}## expression.
I don't see how the expression can be simplified before inserting the limit, that seems out of the question.
I have a few theorems involving points at infinity, but none of them apply here.
I considered making the denominator real by multiplying by its complex conjugate, but the numerator will still be 0 when multiplied by any number.
The answer is supposed to be ##1/(i\sqrt{2})##.
Not looking for a solution or quick fix, would be very happy if someone could help me the first step of the way.J