But since John knew exactly who Jesus was "upon whom thou shalt see the spirit decending," why did he send to ask Jesus this question "art thou he that should come, or do we look for another?" Matthew 10:32
You said Matthew 10:32, but I'm assuming that you meant Matthew 11:3.
John's question was prompted by some things he had heard while in prison.
We read:
Matthew chapter 11
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Now when John had heard in the prison the works of Christ, he sent two of his disciples,
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3] And said unto him, Art thou he that should come, or do we look for another?
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4] Jesus answered and said unto them, Go and shew John again those things which ye do hear and see:
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5] The blind receive their sight, and the lame walk, the lepers are cleansed, and the deaf hear, the dead are raised up, and the poor have the gospel preached to them.
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6] And blessed is he, whosoever shall not be offended in me.
Luke gives us more insight in relation to exactly what John had heard while in prison.
We read:
Luke chapter 7
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1] Now when he had ended all his sayings in the audience of the people, he entered into Capernaum.
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2] And a certain centurion's servant, who was dear unto him, was sick, and ready to die.
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3] And when he heard of Jesus, he sent unto him the elders of the Jews, beseeching him that he would come and heal his servant.
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4] And when they came to Jesus, they besought him instantly, saying, That he was worthy for whom he should do this:
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5] For he loveth our nation, and he hath built us a synagogue.
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6] Then Jesus went with them. And when he was now not far from the house, the centurion sent friends to him, saying unto him, Lord, trouble not thyself: for I am not worthy that thou shouldest enter under my roof:
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7] Wherefore neither thought I myself worthy to come unto thee: but say in a word, and my servant shall be healed.
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8] For I also am a man set under authority, having under me soldiers, and I say unto one, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it.
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9] When Jesus heard these things, he marvelled at him, and turned him about, and said unto the people that followed him, I say unto you, I have not found so great faith, no, not in Israel.
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10] And they that were sent, returning to the house, found the servant whole that had been sick.
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11] And it came to pass the day after, that he went into a city called Nain; and many of his disciples went with him, and much people.
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12] Now when he came nigh to the gate of the city, behold, there was a dead man carried out, the only son of his mother, and she was a widow: and much people of the city was with her.
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13] And when the Lord saw her, he had compassion on her, and said unto her, Weep not.
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14] And he came and touched the bier: and they that bare him stood still. And he said, Young man, I say unto thee, Arise.
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15] And he that was dead sat up, and began to speak. And he delivered him to his mother.
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16] And there came a fear on all: and they glorified God, saying, That a great prophet is risen up among us; and, That God hath visited his people.
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17] And this rumour of him went forth throughout all Judaea, and throughout all the region round about.
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18]
And the disciples of John shewed him of all these things.
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And John calling unto him two of his disciples sent them to Jesus, saying, Art thou he that should come? or look we for another?
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20] When the men were come unto him, they said, John Baptist hath sent us unto thee, saying, Art thou he that should come? or look we for another?
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21] And in that same hour he cured many of their infirmities and plagues, and of evil spirits; and unto many that were blind he gave sight.
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22] Then Jesus answering said unto them, Go your way, and tell John what things ye have seen and heard; how that the blind see, the lame walk, the lepers are cleansed, the deaf hear, the dead are raised, to the poor the gospel is preached.
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23] And blessed is he, whosoever shall not be offended in me.
Apparently, while in prison, John heard how Jesus had healed the centurion's servant (vss. 1-10), how he had raised the widow's son from the dead (vss. 11-15), and how the people were saying in relation to Jesus "that a great prophet is risen up among us, and that God has visited his people" (vs. 16). This "rumour", or word, or report of Christ had spread forth throughout all Judaea, and throughout all the region round about (vs. 17), and it had reached the ears of John the Baptist via his disciples (vs. 18) as well.
Why did these reports cause John to ask, "Art thou he that should come? or look we for another?"
I cannot say for certainty, but it's possible that these types of reports of Christ's mercy and grace seemingly didn't match the revelations that John had personally received in relation to Jesus.
For example, John warned the people to repent and bring forth fruits worthy of repentance or to flee the wrath to come because he saw Jesus as one who would hew down anyone who wasn't bringing forth good fruit and would cast them into fire or burn the chaff or the wicked with unquenchable fire:
Matthew chapter 3
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1] In those days came John the Baptist, preaching in the wilderness of Judaea,
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2] And saying, Repent ye: for the kingdom of heaven is at hand.
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3] For this is he that was spoken of by the prophet Esaias, saying, The voice of one crying in the wilderness, Prepare ye the way of the Lord, make his paths straight.
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4] And the same John had his raiment of camel's hair, and a leathern girdle about his loins; and his meat was locusts and wild honey.
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5] Then went out to him Jerusalem, and all Judaea, and all the region round about Jordan,
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6] And were baptized of him in Jordan, confessing their sins.
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7] But when he saw many of the Pharisees and Sadducees come to his baptism, he said unto them, O generation of vipers, who hath warned you to flee from the wrath to come?
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8] Bring forth therefore fruits meet for repentance:
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9] And think not to say within yourselves, We have Abraham to our father: for I say unto you, that God is able of these stones to raise up children unto Abraham.
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10] And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire.
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11] I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:
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12] Whose fan is in his hand, and he will throughly purge his floor, and gather his wheat into the garner; but he will burn up the chaff with unquenchable fire.
Granted, John also saw Jesus as "the Lamb of God which taketh away the sin of the world" (John 1:29, 36), so he seemingly had some insight or understanding that Jesus would die for the sins of the people.
He also recognized Jesus as the bridegroom who had the bride (John 3:29), but he seemingly was thrown a bit by the compassionate acts that Jesus had been performing.
Whatever the case truly was with John, here was Jesus' reply to his inquiry:
Matthew chapter 11
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4] Jesus answered and said unto them, Go and shew John
again those things which ye do hear and see:
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5] The blind receive their sight, and the lame walk, the lepers are cleansed, and the deaf hear, the dead are raised up, and the poor have the gospel preached to them.
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6]
And blessed is he, whosoever shall not be offended in me.
This was the second time that John would hear such reports ("again" - vs. 4) of his compassionate acts of healing, delivering people from evil spirits (Luke 7:21), and raising people from the dead, and Jesus added that the poor were having the gospel preached unto them as well.
Was John possibly close to being offended in Christ because of his compassionate acts because he was expecting the Messiah to be more of a conquering king?
I don't know.
Was John possibly close to being offended in Christ because of his own imprisonment and impending death which may have caused him to momentarily doubt his own testimonies concerning Christ?
Again, I don't know.
Whatever the case truly was, his question was definitely prompted by the reports he was hearing concerning Jesus' ministry.
I'm sorry, but that's about all that I can say with certainty in response to your question.