Question

"e to the power ix = cos x + i sin x" peove this,​

Answer 1

Answer:

Explanation:

First write out the identities in Taylor's Series for

sin

x

and

cos

x

as well as

e

x

.

sin

x

=

x

−

x

3

3

!

+

x

5

5

!

...

cos

x

=

1

−

x

2

2

!

+

x

4

4

!

...

e

x

=

1

+

x

+

x

2

2

!

+

x

3

3

!

+

x

4

4

!

...

Usually to prove Euler's Formula you multiply

e

x

by

i

, in this case we will multiply

e

x

by

−

i

.

And we will end with

e

−

i

x

thus it will be equal to...

1

+

(

−

i

x

)

+

(

−

i

x

)

2

2

!

+

(

−

i

x

)

3

3

!

+

(

−

i

x

)

4

4

!

...