Coupled differential equation where dependent variable is a complex number

Dear sir , in my problem p(x,t)=po+pd*e^(i*(omega*t+phi1)) and u(x,t)=uo*e^(i*(omega*t+phi2)) i.e. both are function of space variable and time given initial conditions are po,pd,phi1,phi2,uo,omega ,x=[0,2],t=[0,.2] governing equations are dp/dx=(-i*u) and du/dx=(-i*p). here the dependent variables are complex differential equation so this two equations can be converted to 4 real valued equations and 4 initial conditions are given i suspect it will be solved by using ode45. i know how to use ode45 for coupled differential equation where dependent variable is real but not for complex any one please help me thanks in advance.................