**Core Concept**
The Golgi complex, also known as the Golgi apparatus, is a complex organelle found in eukaryotic cells responsible for protein modification, sorting, and packaging. It receives proteins synthesized by the endoplasmic reticulum and modifies them through glycosylation, phosphorylation, and other processes before transporting them to their final destinations within the cell or for secretion outside the cell.

**Why the Correct Answer is Right**
The Golgi complex plays a crucial role in protein modification and sorting by adding carbohydrate (sugar) chains to proteins, a process known as glycosylation. This modification is essential for protein function, stability, and recognition. The Golgi complex also packages proteins into vesicles for transport to lysosomes, the plasma membrane, or for secretion outside the cell. The cisternae of the Golgi complex are stacked like pancakes, and the cisternae are connected by tubular structures called cis and trans elements.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the Golgi complex is not directly involved in the synthesis of proteins; it receives proteins from the endoplasmic reticulum for modification and sorting.
* **Option B:** This option is incorrect because the rough endoplasmic reticulum, not the Golgi complex, is responsible for synthesizing proteins and adding ribosomes for translation.
* **Option C:** This option is incorrect because the lysosomes are organelles responsible for breaking down and recycling cellular waste and foreign substances, not for protein modification and sorting.
* **Option D:** This option is incorrect because the centrioles are involved in the formation of cilia, flagella, and the spindle fibers during cell division, not in protein modification and sorting.

**Clinical Pearl / High-Yield Fact**
The Golgi complex is named after its discoverer, Camillo Golgi, who first described it in 1898. It is a critical organelle in the maintenance of cellular homeostasis, and dysfunction of the Golgi complex has been implicated in various diseases, including glycogen storage diseases and certain types of cancer.

**Correct Answer: C. Lysosomes.