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authorbnewbold <bnewbold@alum.mit.edu>2010-06-30 06:16:45 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-06-30 06:16:45 +0000
commit923d5b4198679221b1a1996747bfcc803352dd70 (patch)
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parentb4dc715e2d88e78600f6c2b48a1c6453166c5c31 (diff)
downloadafterklein-wiki-923d5b4198679221b1a1996747bfcc803352dd70.tar.gz
afterklein-wiki-923d5b4198679221b1a1996747bfcc803352dd70.zip
tex fix?
-rw-r--r--ClassJune26.page3
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@@ -1,4 +1,3 @@
-
Links to Josh's handwritten notes
[link page 1](/L1p1.jpeg)
@@ -162,7 +161,7 @@ We can raise complex numbers to powers, divide by the real denominators,
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
-$\begin{array}ee^{iy} & = & 1+iy+\frac{(iy)^{2}}{2!}+\frac{(iy)^{3}}{3!}+\frac{(iy)^{4}}{4!}+\frac{(iy)^{5}}{5!}+\cdots\\
+$\begin{array}{}ee^{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}$