How do the magnitude and phase spectrum of an imaginary function look like?
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
$$\mathcal F\big\{j \cdot x(t)\big\} = j \cdot \mathcal F\big\{x(t)\big\}$$