**Core Concept**
The patient's presentation of cutaneous vasculitis, glomerulonephritis, and peripheral neuropathy suggests a systemic vasculitic process. This condition is characterized by inflammation of the blood vessels, which can affect multiple organs and systems, including the skin, kidneys, and peripheral nerves.

**Why the Correct Answer is Right**
The investigation that will help diagnose this condition is a test for anti-neutrophil cytoplasmic antibodies (ANCA). ANCA is a type of autoantibody that targets the cytoplasm of neutrophils and is commonly associated with systemic vasculitides such as granulomatosis with polyangiitis (GPA) and microscopic polyangiitis (MPA). These conditions can present with a wide range of symptoms, including cutaneous vasculitis, glomerulonephritis, and peripheral neuropathy. The presence of ANCA can help differentiate these conditions from other types of vasculitis and guide further management.

**Why Each Wrong Option is Incorrect**
**Option A:** A complete blood count (CBC) may show anemia, leukocytosis, or thrombocytopenia, but it will not specifically diagnose the underlying condition. A CBC is a non-specific test that may be useful in monitoring the patient's response to treatment, but it will not provide a definitive diagnosis.
**Option B:** A skin biopsy may show evidence of vasculitis, but it will not provide information about the underlying cause of the condition. A skin biopsy can help confirm the presence of vasculitis, but it will not distinguish between different types of vasculitis or identify the underlying autoantibody.
**Option C:** A renal biopsy may show evidence of glomerulonephritis, but it will not provide information about the underlying cause of the condition. A renal biopsy can help confirm the presence of glomerulonephritis, but it will not distinguish between different types of glomerulonephritis or identify the underlying autoantibody.

**Clinical Pearl / High-Yield Fact**
ANCA-associated vasculitides are a group of systemic vasculitic conditions that are characterized by the presence of ANCA and can present with a wide range of symptoms, including cutaneous vasculitis, glomerulonephritis, and peripheral neuropathy. These conditions are often treated with immunosuppressive therapy, and the presence of ANCA can help guide treatment decisions.

**Correct Answer:** C. A renal biopsy may show evidence of glomerulonephritis, but it will not provide information about the underlying cause of the condition.