How do the magnitude and phase spectrum of an imaginary function look like? Say I have the function
$$x(t)=j \operatorname{rect}(t)$$
Is the phase spectrum even or odd?
I am confused whether the phase spectrum is an odd/even function of $\omega$ (angular frequency, Fourier transform variable).
This might be helpful: https://users.aber.ac.uk/ruw/teach/340/ft_symmetry.php
Your
example is straight forward. You are just multiplying with a constant factor $j$ and that factor carries through the Fourier Transform, i.e. it's simply
$$\mathcal F\big\{j \cdot x(t)\big\} = j \cdot \mathcal F\big\{x(t)\big\}$$