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.