
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

If $\displaystyle z= re^{i\theta}$, then $\displaystyle log(z)= log(r)+ i\theta$. Now think about the fact that adding any multiple of $\displaystyle 2\pi$ does not change z but gives different values for $\displaystyle log(z)$.

right but theres a brannch line