Hi,

I'm doing revision for an exam in complex analysis at the mo. I've been going through examples and I've found a couple that I've never seen before and have no idea how to do-any help would be much appreciated!

a)

Find all values of the following:

$\displaystyle \log\imath$ and log (i+1)

(Can't figure it out in Latex, I'm only learning!)

b) Let D= C\(-oo,0], and suppose log 1=0

Find (1-i)^4i and [e(-1-ROOT(3)i)/2]^(3PIi)

(Again if someone could show me this in latex it'd be appreciated, I kept getting 1-i^4 when I tried)

c)Given D= C\(-oo,0] and $\displaystyle {\imath}^i$=exp(PI/2), its principle value, show that

(-1+(ROOT(3))i)^(3/2)= -2ROOT2

Please help, I'm so confused. I'm thinking it has to do with the section we did on simply connected domains and isolated singularities of an analytic domain

but I can't find any examples to follow and I'm lost!

Thanks

PS I'm trying with the latex but its slow so sorry about that!