At the basic level, your efforts on the given assignment will directly influence the outcome of that assignment. If the assignment is a material one, your boss will be very interested in more than a good outcome for that assignment.
The complexity is generally embedded in the assignment.
The simplicity is (or, should be) demonstrated in the outcome.
When presenting the outcome of your assignment, it is important to choose the right elements of the way you handled the assignment. If you don't, you face the risk of being taken for granted, not getting enough credit for the assignment OR just simply taken advantage of your work. The downside is not normal, but in the rare occasions that happens to you, it can crush your self-esteem.
The choice of how much to include as part of presenting your outcome determines on a few factors that include, but not limited to:
(a) Level of trust that your boss has on you.
(b) Level of competence of your boss on the said topic.
(c) Level of prejudice he or she has.
(d) Your past history with him or her.
For the sake of this discussion, let us take the level of trust your boss has on you. Again, for the sake of simplicity, let us assume that there are only three levels of trust:
(a) Low
(b) Moderate
(c) High
Let us dig deeper into what would make sense for each level.
Low Trust
Your boss needs a LOT more than the right outcome for your assignment as there are many routes to reach the right destination and not all the routes are right. If you have taken a wrong route, there are chances that something else will break in the future. In such cases, it is your responsibility to keep your boss posted on the progress of your assignment with minimum interruption to his work. Intelligently include enough information about your approach to handling the assignment. Your goal is not just to get the right outcome, but also to build up the level of trust for future assignments.
Moderate Trust
In this case, your boss trusts you, but not enough to give you completely free hand. Your approach should be to present the outcome of the assignment along with key inflection points in the journey to complete the assignment. The key thing to include is the rationale behind your decisions at these key inflection points. Once your boss starts to see that your thinking, judgment and reasonings are sound, the level of trust automatically goes up.
High Trust
This is pure gold, but don't take it for granted that it will stay like this for a lifetime. If you screw up once, you might get a pass, but if you screw up more than once, the level of trust drops down like a rock. It will be a Herculean effort to build the trust back. While you can skip the details and present just the outcome, it would help to present any details of the journey where there were learning opportunities for you, your boss or anyone in the organization.