What frequencies are present in the Fourier transform of the Dirac impulse?
A Dirac impulse $x(t)=\delta(t-d)$ has the continuous-time Fourier transform $X(\Omega)$ of
$$\mathcal{F}\{\delta(t-d) \} = 1 e^{-j\Omega d} $$

whose magnitude is $$|X(\Omega)| = 1 ~~~, \text{ for all } \Omega $$ and a phase of $$&lt;X(\Omega) = -\Omega \cdot d $$

Note that it's incomplete to think of the real or imaginary parts of the Fourier transform alone. Rather the magnitude and phase point of views are more reflective of the nature of the result.

So in this case the magnitude is $1$ and hence it's said to contain all frequencies of magnitude $1$. 
Note that these are differential amplitude components of continuum frequency range as opposed to a finite amplitude of discrete set of frequency components, aka line components.