Transcript Euler`s formula

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  
i
e
We get:  cos  i sin 
Since:cos   1 and:sin   0
We get: ei  1
i
e  1
The expantion of e is:
x 2 x3 x 4
e  1  x     ...
2! 3! 4!
x
Let: x  i
2
3
4
(
i

)
(
i

)
(
i

)


 ...
We get ei  1  i 
2!
3!
4!
2
3
4

i


i

Which is: e  1  i     ...
2!
3!3 45! 7
Separate to get:
3
5
i
e  i( 
7

3!


5!
Because:i(  3!  5!  7!  ...)  0 And:
We get ei  1


 ...)  (1 
2

4

6
7!
2! 4! 6!
2
4

 6
(1 

 ...)  1
2! 4! 6!
...)
i
e  1
Proof that there is a God, and that
Matthew James Leech is WRONG!!!!