I am faced with the following question:
Prove that this is an inner product on V.
I understand to show something is an inner product I must verify the following conditions:
$\langle\,f,g\rangle = \overline{\langle\,g,f\rangle}$ (Conjugate symmetry)
$\langle\,\overline\alpha (f + g),h\rangle = \overline\alpha(\langle\,f,h\rangle + \langle\,g,h\rangle)$ (Linearity in the first argument)
$\langle\,f,f\rangle \ge 0$ with equality iff $f=0$
(Note: conditions (1) and (2) are slightly different to usual as we are dealing with complex numbers)
I have seen other examples of this being done, however, I am not sure how to do it in this particular case. Any help with this would be greatly appreciated.