To calculate this intensity pattern, one needs to introduce some more sophisticated methods. The mathematical representation of a radial wave is given by E ( r ) = A cos ⁡ ⁡ ( k r − − ω ω t + ϕ ϕ ) / r where k = 2 π π λ λ , λ λ is the wavelength, ω ω is frequency of the wave and ϕ ϕ is the phase of the wave at the slits at time t = 0. The wave at a screen some distance away from the plane of the slits is given by the sum of the waves emanating from each of the slits. To make this problem a little easier, we introduce the complex wave Ψ Ψ , the real part of which is equal to E Ψ Ψ ( r ) = A e i ( k r − − ω ω t + ϕ ϕ ) / r E ( r ) = Re ⁡ ⁡ ( Ψ Ψ ( r ) ) The absolute value of this function gives the wave amplitude, and the complex phase of the function corresponds to the phase of the wave. Ψ Ψ is referred to as the complex amplitude. With N slits, the total wave at point x on the screen is Ψ Ψ total = A e i ( − − ω ω t + ϕ ϕ ) ∑ ∑ n = 0 N − − 1 e i k ( x − − n a ) 2 + L 2 ( x − − n a ) 2 + L 2 .