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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