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#1 2009-01-22 09:41:06

jasontkj
Member
Registered: 2009-01-22
Posts: 1

(1+i)^i

i denotes the imaginary number .
So how can i compute (1+i)^i??

Thanks!!

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#2 2009-01-22 09:54:20

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: (1+i)^i

I guess writing (1+i) in exponential form would help a lot.

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#3 2009-01-22 10:03:45

careless25
Real Member
Registered: 2008-07-24
Posts: 560

Re: (1+i)^i

so Kurre

(1 + -1^.5)^-1^0.5?

This is confusing me...

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#4 2009-01-22 11:30:11

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: (1+i)^i

By exponential form, Kurre means use the relationship:

Last edited by Daniel123 (2009-01-22 11:31:08)

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#5 2009-01-22 12:37:59

Muggleton
Member
Registered: 2009-01-15
Posts: 65

Re: (1+i)^i

for all integers n. The principal value is when n = 0.

Last edited by Muggleton (2009-01-22 12:40:30)

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#6 2009-01-22 13:55:29

careless25
Real Member
Registered: 2008-07-24
Posts: 560

Re: (1+i)^i

i still need to learn all that....mind explaining?

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#7 2009-01-23 03:54:21

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: (1+i)^i

careless25 wrote:

i still need to learn all that....mind explaining?

Look at the series expansions of e^x, and let x = iθ (simplify a bit)

Compare this to the series expansions of cosx and sinx. You should be able to see why e^iθ = cosθ + isinθ.

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