Calculus Question about Exponentials

[us3rnotfound]

Why is e^i2pi, e^i4pi, e^i6pi, etc = 1?

I think it is because of Euler's Rule, which would make e^i2pi = cos(2pi) + isin(2pi)
= 1 + i0 = 1. Is this the exact reasoning?

Are there any good websites specifically on exponentials? I am very bad at them and I am in EE so I need to know them really well.

Thanks AT.

 

[Gibson486]

Originally posted by: us3rnotfound
Why is e^i2pi, e^i4pi, e^i6pi, etc = 1?

I think it is because of Euler's Rule, which would make e^i2pi = cos(2pi) + isin(2pi)
= 1 + i0 = 1. Is this the exact reasoning?

Are there any good websites specifically on exponentials? I am very bad at them and I am in EE so I need to know them really well.

Thanks AT.

yes, you stated the reason. look at the imaginary circle and you see why.

 

[JohnCU]

also i is current, j is imaginary, get it right

 

[Gibson486]

Originally posted by: JohnCU
also i is current, j is imaginary, get it right

it depends who you ask. mathematicians like i, EE's like j. it's just a place hold holder. You could call e^(suck_my....*t) and still get the same result.

 

[JohnCU]

Originally posted by: Gibson486

Originally posted by: JohnCU
also i is current, j is imaginary, get it right

it depends who you ask. mathematicians like i, EE's like j. it's just a place hold holder. You could call e^(suck_my....*t) and still get the same result.

he said was in EE so he better learn to like j. also it's easier for them to switch than us. we made our calc teacher use j.

 

[polarmystery]

Originally posted by: us3rnotfound
Why is e^i2pi, e^i4pi, e^i6pi, etc = 1?

I think it is because of Euler's Rule, which would make e^i2pi = cos(2pi) + isin(2pi)
= 1 + i0 = 1. Is this the exact reasoning?

Are there any good websites specifically on exponentials? I am very bad at them and I am in EE so I need to know them really well.

Thanks AT.

http://en.wikipedia.org/wiki/Euler's_identity
http://en.wikipedia.org/wiki/L...igonometric_identities

2pi, 4pi, and 6pi satisfy the equation making it a complete circle. The equation is actually not 2pi, but theta (or phi, whatever angle you want) in place of 2pi in your first formula with sin/cosine. These equations:

cos(x) = (e^jx + e^-jx)/2
sin(x) = (e^jx - e^-jx)/2j

will follow you everywhere in EE. Learn them...learn them well.