Could someone please help get me started on this problem?

For part (a), I always took for granted as if it were by definition but maybe it's defined in the regular xy plane and then deduced in the polar form? If I'm right, how do I start specifically? If I'm wrong then what do I do?

As for part (b), that's just applying part (a) mechanically, right?

Any help in solving this problem would be greatly appreciated!

Thanks in advance!