how to plot amplitude spectrum of complex signal

I am taking a pulse p(t) having Fourier transform as P(f) . Then delaying the same pulse by delta so that its Fourier transform becomes P(f). exp(-j2*pi*f*delta). Now adding the two Fourier transforms gives P(f)[1+exp(-j*2*pi*f*delta)]. If we assume their sum is zero , then 1 = exp(-j*2*pi*f*delta) . This is solved for the product f*delta. Now for a fixed delta , we get a particular value of f say fn such that the composite Fourier transform has zero values at those fn. I want to show the same using MATLAB , but the problem is that whenever I take the fft of both pulses , the absolute values are same and the sum is 2 times of individual response . Theoretically we should be able to obtain the graph showing zero at fn for a specific value of delta , and I want to plot the same. How can this be done ?