If you have a complex baseband signal
and you multiply it with a (real-valued) sinusoid, the resulting signal is obviously still complex. What happens in IQ-modulation is that you generate a real-valued band-pass signal containing the same information as $x(t)$:
Using the magnitude and phase of $x(t)$, the bandpass signal $s(t)$ can also be written in the form
which shows that in general $s(t)$ is amplitude and phase modulated.
This is what happens in the frequency domain when you use a sinusoid for modulation as opposed to IQ modulation. Let
In the frequency domain this corresponds to
For the IQ modulated signal $s(t)$ we get (from $(2)$)
The Fourier transform of $(6)$ is
Comparing $(5)$ and $(7)$ you see that the part of the spectrum that is centered around $-\omega_c$ is inverted for $s(t)$ (i.e., it is a mirror image of $X(j\omega)$; note the negative sign before $j$), whereas it is just shifted without inversion for the cosine modulated signal $r(t)$.