How to create an invoice with status "complete"

Question

I have a function which is creating an invoice, just the status of the invoice created is "pending". How can I create the invoice with the status "Complete"?

$invoice = Mage::getModel('sales/service_order', $order)->prepareInvoice();

if (!$invoice->getTotalQty())
    Mage::throwException(Mage::helper('core')->__('Cannot create an invoice without products.'));

$invoice->setRequestedCaptureCase(Mage_Sales_Model_Order_Invoice::STATE_PAID);
      $invoice->register();
$transactionSave = Mage::getModel('core/resource_transaction')
    ->addObject($invoice)
    ->addObject($invoice->getOrder());

 $transactionSave->save();

CE 1.9

Answer 1

I solved with the following code

$invoice->setState(Mage_Sales_Model_Order_Invoice::STATE_PAID);