Waste less time on Facebook — follow Brilliant.
×

Do you know De Moivre's formula ?

As we know \(\sqrt{1}=1\) But we know too that \(cis(2π)=1\), so we can take the square root and find that \(\sqrt{cis(2π)}=\sqrt{1}\). By De Moivre's formula \(cis(π)=1\) or \(cis(2π)=1\) \(=> -1=1\) or \(1=1\). What's wrong with it??

Note by Hjalmar Orellana Soto
2 years, 4 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Is it something to do with the fact that you have to take the positive root when dealing with complex numbers? I know \(\sqrt{ab} = ( \sqrt{a}) \times\ ( \sqrt{b}) \) isn't applicable to complex numbers, but I'm not sure if that proves useful here.

Curtis Clement - 2 years, 4 months ago

Log in to reply

See here.

Micah Wood - 2 years, 4 months ago

Log in to reply

So, what happens with this? \(e^{ix}=cis(x)\) \(=>(e^{ix})^{k}=(cis(x))^{k}\) \(=>e^{i(kx)}=cis(kx)\) \(=>(cis(x))^{k}=cis(kx)\) For every real \(k\) this should work.

Hjalmar Orellana Soto - 2 years, 4 months ago

Log in to reply

Do you mean: \[\ Cis( \phi ) = Cos( \phi ) + iSin( \phi ) \ ? \ ... (i = \sqrt{-1} ) \]

Curtis Clement - 2 years, 4 months ago

Log in to reply

Yes

Hjalmar Orellana Soto - 2 years, 4 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...