sqrt.php

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<?php

namespace Complex;

if (!function_exists(__NAMESPACE__ . '\\sqrt')) {
    function sqrt($complex): Complex
    {
        $complex = Complex::validateComplexArgument($complex);

        $theta = theta($complex);
        $delta1 = \cos($theta / 2);
        $delta2 = \sin($theta / 2);
        $rho = \sqrt(rho($complex));

        return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix());
    }
}