I have dealt with the issue before, "Is God complex?" about a year ago. I'm not satisfied with my answer because I got off on a tangent. The idea that God is complex and that somehow that disproves God or makes it harder to believe in God, is all over the place, ever atheist message board, on thousands of pages it a standard myth of their propaganda. Having dealt with it again recently I feel like it's time to give it a good bash.
Take the view point of Richard Dawkins in his most celebrated work The God Delusion. 
The argument from improbability is the big one. In the traditional guise of the argument from design, it is easily today’s most popular argument offered in favor of the existence of God, and it is seen, by an amazingly large number of theists, as completely and utterly convincing. It is indeed a very strong, and, I suspect, unanswerable argument—but in precisely the opposite direction form the theist’s intension. The argument from improbability, properly deployed, comes close to proving that God does not exist…
This quotation tells us several very important things about the manner in which the major leader of the new atheist movement thinks. The first thing this quotation tells us is that Dawkins’ views evolution as an atheist territory, he doesn’t think of evolution as a theistic possibility, he can only conceive of belief in God being the domain of people who can’t understand evolution. He thinks of God belief as strictly creationist territory. He basically says as much in following up this quotation above he talks about the analogy of a 747 being assembled by random chance from a junk yard. “This in a nutshell is the creationist favorite argument.” He doesn’t say there are other theological views and he doesn’t deal with them, as though they don’t exist. One might forgive this tendency if he thinks liberal theology is just out of the main stream and thus beyond the focus of the popular audience. Nevertheless he goes even further, “It turns out to be the God hypothesis that tries to get the free lunch…however statistically improbable the entity you seek to explain by evoking a designer, the designer himself has got to be at least as improbable. God is the ultimate 747.”
He is doing more than just reversing the design argument he’s trying to apply the logic of the design argument to a critique of belief in God. This led to the often repeated refrain on message boards and blogs, “who designed the designer?” That’s not exactly what he’s saying either. He is establishing the idea that God has to meet the same requirements of probability that nature has to meet as an alternative to God. The point here, however, is that he is enabled to make this argument by the badly misconstrued nature of theology in the evangelical camp. That misconstrual allows for an application of the same principle to God that we take to examining nature. He is treating God like a big man in the sky. Is God subject to the laws of probability? It is the fundamentalist tendency to think of God as a big man in the sky rather than the foundation of all that is, that conditions the atheist appraoch. When we think of God as “creator” and “designer” rather than “ground of being” we put God in the category to be analyzed by the laws of probability. There is no logical reason why the ground of being could be analyzed as though it is just another thing in creation alongside flush toilets and swizzle sticks. In reality, God is not probable at all. The word “complex” is meaningless when used of the basis of all that is. “Complex” is a relative term. A jigsaw puzzle is complex compared to a baby’s building blocks. It may be child’s play compared to a printed circuit or higher mathematics. This is like trying to apply up and down, north, south, east, and west in outer space. Which way is up when there’s no down? Which way is west when there’s no horizon? The creationists really put the misconception in motion by thinking of God a “designer.” It would have been better to peserve the truth of God that the church fathers taught us, that God is beyond our understanding. In their haste to produce an argument that would impress modern science the apologists (William Paley before him Newton and Boyle) tried to ground proof in empirical data and succeeded only in creating the impression, perhaps even against their own beliefs, that God can be thought of analogously to a big man in the sky. Dawkins is not going to work very hard at correcting the impression. Through the ground of being concept we can realize God’s reality without having to rely upon data or empirical scientific observations to know that God is real.
Official Christian doctrine says God is simple:
God is not composed or divisible by any physical or metaphysical means. Simplicity of God refers to the fact that he has no parts. The simplicity teaching extends to the entire nature of God. His substance, nature, and very being is that of utter simplicity. The properties usually attributed to God such as omnipotence, omniscience and omnipresence do not contradict the teaching of simplicity because each property is a different way of looking at the infinite active being of God from a limited perspective. One consequence of this teaching is the fact that since God is simple, he must be a pure spirit.
- Definition of the Dogma:
The dogma of simplicity follows from the teachings of the 4th Lateran Council and the first Vatican Council which stated that God is an absolutely simple substance or nature. The basis of this De Fide dogma can be found within the gospel of John, "God is a spirit" (John 4:24).
- Heresies which reject or confuse this teaching:
Anthropomorphism (the heresy of believing God has a body) violates the dogma of simplicity. Anthropomorphism, latent in Mormonism, paganism and polytheism fails to consider the fact that God exists in complete and total actuality. Since God has not unrealized potentiality in the metaphysical sense, he cannot possibly have parts or a body.Atheists are now arguing that if God is mind and God imagines the world then that would make God complex, becuase it's a complex mind that has a lot of stuff in it. But that's assuming the kind of mind that is supported by a physical brain and that needs dendrites to house memory. There is no proof that a purely mental reality would would be complex. Minds can have an infinite number of things in them and not take up any room.
Additionally, pantheism, New Age religions and some of the more naiveté Christian sects tend to view God as a diffuse metaphysical being that permeates nature and gives nature a certain metaphysical share in divinity. Such a doctrinal stance violates the teaching of God’s simplicity by assuming that nature has a metaphysical share in God’s nature. The creations of God can play no part in his metaphysical being without violating his simplicity.
Even if we wanted to accept that God is complex why would it have the same consequences that Dawkins argues for it? When Dawkins says that complexity is less likely than simplicity he's assuming an evolutionary process. God is not the product of an evolutionary process. Because Dawkins assumes an evolutionary process he also assumes a flesh and blood organism, and God is not that either. There is no evidence for a mental being to be complex it would produce any kind result that would impare God's existence.
 Richard Dawkins, The God Delusion. New York: First Marionor books, Houton Mifflin Company, 2008 first published in Great Britain by Bantam, 2006. On line version Google Books URL: http://books.google.com/books?id=Ayt0bUwN5v4C&printsec=frontcover&dq=Dawkins+from+the+God+Delusion&source=bl&ots=6M_E5W8-Uo&sig=j5bAGhDSY6MGYxYeQpv_q8T3l_A&hl=en&ei=gPKATLvvHsHflgeNgKHnDg&sa=X&oi=book_result&ct=result&resnum=6&ved=0CDkQ6AEwBQ#v=onepage&q&f=true
 Ibid. online page number 138 all quotations from this source are from the Google books online version.