"燃起复仇念头的" can be translated into English as "consumed by a desire for revenge" or "seized by a vengeful notion".
Here are some example sentences for context:
1、 After the tragedy, he was consumed by a desire for revenge.
（悲剧发生后，他燃起了复仇的念头。）
2、 The betrayal left him seized by a vengeful notion.
（那次背叛让他燃起了复仇的念头。）
Both expressions convey the idea of someone being deeply affected by a strong feeling of wanting to seek revenge. Choose the one that best fits the context and tone of your sentence.