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Learning about Stardust

Talk to Leon in Atlantis.
 

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Introduction

Like gems, Stardust can be used to improve your gear. Soul Gear from instances can have an insignia placed on it, then you can imbue matching stardust into the gear.

NPC Dialog

I think it is time you learned about Stardust. Stardust is a mystical powder, with magical effects comparable to gems. Stardust can only be imbued into very special gear, however, only Soul Gear can be imbued in this way.

Quest Completion

You need real soul gear. I can take a look at it, then Dyana can teach you about Stardust.