The Christian doctrine concerning Jesus' two natures is called the hypostatic union. It is the teaching that the Divine Word of God (John 1:1) "became flesh and dwelt among us," (John 1:14). Therefore, Jesus is both divine and human in one person (Col. 2:9); He has two natures: human and divine. But some who oppose the Trinity and Jesus' incarnation (the Divine Word becoming a man), say that if Jesus is God in flesh this must mean that God's nature changed because God added a human nature to His divine nature. This would violate Malachi 3:6 which says that God does not change. But, the union of the two natures of Jesus in one person does not constitute a change in the nature of God.
Since the hypostatic union teaches that in the one person of Jesus there are two natures, the divine nature of Jesus is not affected by union with the human nature because there is no fusion of the two natures. That is, the divine nature is not combined with the human nature to make a third thing. This would be the error known as monophysitism. Jesus is not a new third thing with a fused-together new nature. Instead, it is a union. An example of a union is marriage between a man and a woman. Each is separate, but in marriage "...they shall become one flesh," (Gen. 2:24), yet they remain two distinct individuals. They are not blended into a new third thing. Fusion, on the other hand, can be illustrated by combining copper and zinc together to form a new third thing called brass. In this case, the two elements lose their identity and are merged together into something new. But in a union, the elements do not lose their identity or nature. The hypostatic union is not a hypostatic fusion and the two natures of Jesus do not lose their distinction and they are not altered.
Furthermore, within the union of the two natures in the one person of Christ, the divine nature is still divine and the human nature is still human. One is not altered by the presence of the other anymore than my spirit in me is altered in nature by its indwelling a physical body. Likewise, the divine Word is not altered by indwelling human flesh.
Finally, the doctrine of the Trinity is that God is three persons: Father, Son, and Holy Spirit. This does not mean three gods. There is only one God. The Trinitarian nature of God is not altered by the union of the Word with humanity since it was the divine Word that humbled Himself to become a man (John 1:1,14; Phil. 2:5-8), not the Father or the Holy Spirit. Therefore, by definition, the Trinity is unaffected by the union of the Word with humanity in the incarnation of Jesus.