# log(z+3i)

• Mar 1st 2010, 01:02 PM
wowsomeme
log(z+3i)
hey guys... this is a two part question

1. where is the log not analytic

ok so i know its where the Re is less than or equal to 0
and where the Im =0

so i preety much just write log(x+iy+3i)
and equate.. how ever its asking for the log... not the Log

so how do i do that

and lastly how woud i take the log(z+3i)

do i write it as log(re^i@ +3i)

and do ln(r) +.....??

thanks for all the help
• Mar 1st 2010, 01:32 PM
HallsofIvy
If $z= re^{i\theta}$, then $log(z)= log(r)+ i\theta$. Now think about the fact that adding any multiple of $2\pi$ does not change z but gives different values for $log(z)$.
• Mar 1st 2010, 01:39 PM
wowsomeme
right but theres a brannch line