Math 2.0

Special functions Corollary

Euler's identity

Builds on Euler's formula

Statement

eiπ+1=0.e^{i \pi} + 1 = 0.

Remarks

Proof: Euler's formula with z=πz = \pi gives eiπ=cos⁡π+isin⁡π=−1e^{i \pi} = \cos \pi + i \sin \pi = -1. The identity links five constants: 00, 11, π\pi, ee and ii.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

Show the path as a graph
Complex numbers, object, no evidence levelComplex numbersobjectEuler's formula, statement, no evidence levelEuler's formulastatementEuler's identity, statement, no evidence levelEuler's identitystatement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Complex numbers object
  2. Euler's formula statement
  3. Euler's identity statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Euler%27s_identity, lead section
About this page
Tag09285XX7AE
URIm2://09285XX7AE
Kindstatement, corollary
WritingW1 stated
MSC33B10
StatusThis copy of the site has no build data. Run m2 status 09285XX7AE.
UsesEuler's formula
Same as

Markdown · JSON · Edit on GitHub

What this page needs for W2

  • edge about out: the concepts that the statement is about (0 of 1)
  • edge proves in: at least one proof node (0 of 1)
  • edge instance_of or illustrates in: one example that shows the statement at work (0 of 1)
  • explanation L2 (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.