Math Is Fun Forum

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!!

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: (1+i)^i

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

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...

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)

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)

careless25

Real Member

Registered: 2008-07-24

Posts: 560

Re: (1+i)^i

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

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: (1+i)^i

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.