How can the bcmath extension in PHP help in achieving more accurate results in complex number calculations?

Complex number calculations often involve floating-point arithmetic, which can lead to rounding errors and inaccuracies. By using the bcmath extension in PHP, which provides arbitrary precision arithmetic, we can achieve more accurate results in complex number calculations by performing calculations with higher precision.

// Enable the bcmath extension
extension_loaded('bcmath') or die('Error: bcmath extension not loaded');

// Set the scale for bcmath calculations
bcscale(10);

// Perform complex number calculation with bcmath
$real1 = '1.23456789';
$imaginary1 = '2.34567890';
$real2 = '3.45678901';
$imaginary2 = '4.56789012';

$sum_real = bcadd($real1, $real2);
$sum_imaginary = bcadd($imaginary1, $imaginary2);

echo "Sum: " . $sum_real . " + " . $sum_imaginary . "i";