Question

We____definitely look into the matter", the officer affirmed.​

Answer 1

Answer:

We____definitely look into the matter", the officer affirmed.

• We will definitely look into the matter", the officer affirmed.
• Will is the right answer.

Explanation:

• "We will definitely look into the matter", the officer affirmed. - It is a direct speech and we can turn it into an indirect speech : The officer affirmed that they would definitely look into the matter.
• When direct speech turns into indirect speech then will turns into would and shall turns into should.

• Shall and will are auxiliary verbs of Future Indefinite Tense.
• Examples: I shall wait for you . He will give me a pen.

Answer 2

Answer: WILL

Explanation:

We_will___definitely look into the matter", the officer affirmed.​

The word WILL make the above sentence grammatically correct and meaningfully complete to understanding the literal meaning properly.

WILL is a modal verb used in forming the future tenses i.e. something which is impending to happen.

For eg., The doctor will be calling next week to check on the patient's progress.

Hope it helps!