solving partial differential equations using complex numbers

hi there folks,

what i wanted to ask today is the following :

i know that complex numbers can be used to simple differential equations of the second order such as 10y''+y'+1=0

my question is this , lets take a partial differential equation such as the wave equation (for those not familiar http://upload.wikimedia.org/math/b/d...9f7a8ddda6.png )

now , given the proper initial values , or an adequate set of boundary limits i can guess a solution , quantimize(spelling?) it and find a soltuion for the equation dependant on n,x,t

my question is the following , i know that some people will prefer to solve such an equation using complex numbers, so my request is this , could someone provide an example to doing so ? any partial differential equation will do , i only gave the wave equation as an example.