I have currently started solving the exercises from the book Functions of one complex variable by J.B. Conway.This is a problem from the exercise of Chapter 1.It looks very simple and I can imagine it very well but having problem to get an analytical solution. Any help will be truly appreciated.
asked Oct 16, 2016 at 18:52
jyoti prokash roy jyoti prokash roy
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$\begingroup$ What do S and N stand for ? Is it the Riemann sphere its north pole ? $\endgroup$
Commented Oct 16, 2016 at 18:59
$\begingroup$ Hint: intersection of the planes is a line in $\mathbb
Commented Oct 16, 2016 at 19:03
$\begingroup$ @Astyx ,S is the unit sphere and N is its north pole. $\endgroup$
Commented Oct 16, 2016 at 20:09
$\begingroup$ Yes I can imagine that but need some analytical proof. $\endgroup$
Commented Oct 16, 2016 at 20:11
$\begingroup$ The dimension of a plane in $\Bbb R^3$ is 2, thus the dimension of the intersection of 2 planes is at most 2. If it was 2, you would have $\Bbb C = P$ which is obviously not true since $S \cap \Bbb C = \$. Therefore the intersection is a line. $\endgroup$
Commented Oct 16, 2016 at 20:16
