$\ln (z+i)=0, z+i=t, \ln t = 0; t= e^{\ln|t| + i\varphi},\\
\mbox{sledi}\ \ln t = \ln|t| + i\varphi = 0 = 0 + 0i\\
\mbox{sledi}\ \ln|t|=0, \varphi = 0,\ \mbox{sledi}\ |t|=1, \varphi=0, \mbox{sledi} \ t=1, z=t-i, \textbf{z=1-i}. $