**Core Concept**
Deep vein thrombosis (DVT) is a condition characterized by the formation of a blood clot in a deep vein, typically in the legs. Establishing a diagnosis of recurrent DVT requires a combination of clinical evaluation, imaging studies, and laboratory tests to rule out underlying conditions that may predispose the patient to thrombosis.

**Why the Correct Answer is Right**
In a patient with recurrent DVT, it is essential to investigate for underlying conditions that may increase the risk of thrombosis, such as inherited or acquired thrombophilias. These conditions can be identified through laboratory tests, including coagulation studies, genetic testing, and assessment of inflammatory markers. The correct investigations will help to determine the underlying cause of the patient's recurrent DVT and guide appropriate management.

**Why Each Wrong Option is Incorrect**
**Option A:**
This option is incorrect because D-dimer levels are often elevated in patients with DVT, but they are not specific for the diagnosis. A positive D-dimer can be seen in various conditions, including infection, inflammation, and malignancy.

**Option B:**
This option is incorrect because imaging studies, such as Doppler ultrasound or CT venography, are essential for diagnosing DVT. These studies can help to visualize the clot and determine its location and extent.

**Option C:**
This option is incorrect because a complete blood count (CBC) can help to identify underlying conditions that may increase the risk of thrombosis, such as polycythemia vera or leukemia. However, a CBC is not specific for the diagnosis of DVT.

**Option D:**
This option is incorrect because a chest X-ray is not typically used to diagnose DVT. While a chest X-ray may be performed to evaluate for pulmonary embolism, which can occur as a complication of DVT, it is not a primary investigation for DVT.

**Clinical Pearl / High-Yield Fact**
In patients with recurrent DVT, it is essential to investigate for underlying conditions that may increase the risk of thrombosis, such as inherited or acquired thrombophilias. This can help to guide appropriate management and reduce the risk of future thrombotic events.

**Correct Answer: C. A complete blood count (CBC) can help to identify underlying conditions that may increase the risk of thrombosis, but it is not specific for the diagnosis of DVT.**