# Euler's formula by sa6662B

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```									 Euler's formula

i
e  1
Leonhard Euler
Euler was one of
the most popular
mathematicians of
all time. He made
important
breakthroughs in
fields such as
calculus and graph
theory.
e
E is a constant value that is the base of a natural
logarithm. Its exact value to 20 decimal places is
2.71828 18284 59045 23536...
When differentiated or integrated the value of e to
the power of x will remain the same.
i
i is an imaginary number that allows the real
number system to be extended into the complex
number system. It is better known as the square
root of –1.
i is one of few values that when squared will
equal negative 1

Pi is one of the most popular numbers used in
mathematics, particularly when looking at circles.
Its main use is showing the ratio of the
circumference of a circle to its diameter.
The value of pi to 20 decimal places is 3.14159
26535 89793 23846, but it can be calculated to
over a trillion decimal places.
i
e  1
We know that: eix  cos x  i sin x
Let: x  
We get:   ei  cos  i sin 
Sincecos  1 and:sin   0
:
We get: ei  1
i
e  1
x 2 x3 x 4
The expantion of e is:                e  1  x     ...
x

2! 3! 4!

Let: x  i
(i ) 2 (i )3 (i ) 4
We get ei  1  i                        ...
2!      3!      4!
 2 i 3  4
Which is: e  1  i     ...
i

2!   3!3 4! 7
i
5
                                       2       4       6
Separate to get:            e  i (                             ...)  (1                         ...)
3!       5!      7!            2! 4! 6!
3   5   7                                   2
 4
6
Because:i(  3!  5!  7!  ...)  0 And:                 (1            ...)  1
2! 4! 6!

We get ei  1
i
e  1

Proof that there is a God, and that
Matthew James Leech is WRONG!!!!

```
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