Andrew's git
/
notes.git
/ diff
summary
|
log
|
commit
| diff |
tree
commit
grep
author
committer
pickaxe
?
re
complex roots
author
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 25 Feb 2019 11:41:54 +0000
(22:41 +1100)
committer
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 25 Feb 2019 11:41:54 +0000
(22:41 +1100)
spec/complex.md
patch
|
blob
|
history
raw
|
patch
| inline |
side by side
(parent:
0bc414a
)
diff --git
a/spec/complex.md
b/spec/complex.md
index 871e1d43c7d113963ac32c901d829c2210b29f70..d1119212a4abd95e20212ac5a80366afd567bde2 100755
(executable)
--- a/
spec/complex.md
+++ b/
spec/complex.md
@@
-150,3
+150,10
@@
${z_1 \over z_2} = {r_1 \over r_2} \operatorname{cis}(\theta_1-\theta_2)$ (divid
## de Moivres' Theorem
$(r\operatorname{cis}\theta)^n=r^n\operatorname{cis}(n\theta)$ where $n \in \mathbb{Z}$
+
+## Roots of complex numbers
+
+$n$th roots of $r \operatorname{cis} \theta$ are:
+$z={r^{1 \over n}} \cdot (\cos ({{\theta + 2k \pi} \over n}) + i \sin ({{\theta + 2 k \pi} \over n}))$
+
+Same modulus for all solutions. Arguments are separated by ${2 \pi} \over n$
\ No newline at end of file