Ice Imbue - Slows down enemies with Frostbite, or Freezes them for a short amount of time.
Lighting Imbue - Reduces the enemies Parry Ratio which you can do more damage to them over time.
Fire Imbue - Once the enemy is Burned, the Burn effect does damage to them over a period of time.
And yes, Fire Imbue is a good choice as a Nuker. It does the most damage which is really good if you want to kill some1 faster in PvP, Its also good in PvE. And yes when you Use Imbues, it does Effect your Nukes which makes you do more damage (or so i've heard).
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How far should I go with the fire imbue, max first two books or go all the way? Same question for lightning?
You should max out all the Fire Imbue books, but you should leave the Lighting Imbue alone, unless you have Extra SP for it.