Step 1: Pleuritic chest pain in an immobilized patient strongly suggests pulmonary embolism, supported by dyspnea, tachypnea, and possible hemoptysis.
Step 2: The aim of imaging is to visualize the clot within the pulmonary arteries quickly and reliably.
Step 3: Contrast-enhanced CT (CT pulmonary angiogram) directly images the filling defect of the embolus, is non-invasive, and has largely replaced conventional pulmonary angiography in routine practice, so it is the most helpful technique here.
Step 4: Plain chest radiograph and ultrasound lack sensitivity for clot, and the V/Q scan is a backup when CT or contrast is contraindicated. Therefore the CT scan is selected.
\[\boxed{\text{CT scan}}\]