[Need Help With Logo]

So, if I zoom in like 2 clicks, where the silver meets the blue the curved lines are "choppy".  Not a smooth curve like I would expect.  Also, where the light silver meets the darker silver.  Maybe, that's just how it is...and, maybe, the it becomes more distorted the more you zoom in.  I don't know, but I'm willing to learn what's up.

[Need Help With Logo]

I can not figure out how to smooth out the pixelated-type edges on the logo that I have attached.  Is there any way to make the curved edges smooth?  I have watched countless tutorials and tried many of the various plug-ins, but can't actually get it to work myself.

 

Thank you in advance for any advice posted.