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author | joshuab <> | 2010-06-29 15:24:17 +0000 |
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committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-06-29 15:24:17 +0000 |
commit | 45a4bb100ca5aea14554f265ffc09e981d79a36c (patch) | |
tree | 8869b17143ac4b87164baeedce0d64b547277b0f /ClassJune26.page | |
parent | d4481a0d023cacf22a1dcf9a35324ba5a42c63f6 (diff) | |
download | afterklein-wiki-45a4bb100ca5aea14554f265ffc09e981d79a36c.tar.gz afterklein-wiki-45a4bb100ca5aea14554f265ffc09e981d79a36c.zip |
tex
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-rw-r--r-- | ClassJune26.page | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/ClassJune26.page b/ClassJune26.page index faa516c..15c603a 100644 --- a/ClassJune26.page +++ b/ClassJune26.page @@ -153,7 +153,7 @@ and add them up just fine, so we can exponentiate complex values of $z$. We know what happens to real values, what happens to pure imaginary ones? Let $y\in\mathbb{R}$. Then $\begin{array} -e^{iy} & = & 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ + e^{iy} & = & 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\ & = & 1+iy-\frac{y^{2}}{2!}-i\frac{y^{3}}{3!}+\frac{y^{4}}{4!}+i\frac{y^{5}}{5!}+\cdots\\ & = & (1-\frac{y^{2}}{2!}+\frac{y^{4}}{4!}+\cdots)+i(y-\frac{y^{3}}{3!}+\frac{y^{5}}{5!}-\cdots)\\ & = & \cos y+i\sin y\end{array}$ |