/**
 * Given two complex numbers in polar form, z1 and z2,
 * this function determines if the absolute value of z1 is greater than or equal to the absolute value of z2.
 *
 * @param z1 A pair representing the polar form of z1, where the first element is the magnitude and
 *           the second element is the argument (in radians).
 * @param z2 A pair representing the polar form of z2, where the first element is the magnitude and
 *           the second element is the argument (in radians).
 * @return True if the absolute value of z1 is greater than or equal to the absolute value of z2,
 *         otherwise False.
 */
fun polarGreaterEqual(z1: Pair<Double, Double>, z2: Pair<Double, Double>): Boolean {

    val (r1, theta1) = z1
    val (r2, theta2) = z2

    // Calculate the absolute values for z1 and z2
    val absZ1 = Math.abs(r1)
    val absZ2 = Math.abs(r2)

    // Check if absZ1 is greater than or equal to absZ2
    return absZ1 >= absZ2
}
/**
 * Given two complex numbers in polar form, z1 and z2,
 * this function determines if the absolute value of z1 is greater than or equal to the absolute value of z2.
 *
 * @param z1 A pair representing the polar form of z1, where the first element is the magnitude and
 *           the second element is the argument (in radians).
 * @param z2 A pair representing the polar form of z2, where the first element is the magnitude and
 *           the second element is the argument (in radians).
 * @return True if the absolute value of z1 is greater than or equal to the absolute value of z2,
 *         otherwise False.
 */
fun polarGreaterEqual(z1: Pair<Double, Double>, z2: Pair<Double, Double>): Boolean {
/**
 * Given two complex numbers in polar form, z1 and z2,
 * this function determines if the absolute value of z1 is greater than or equal to the absolute value of z2.
 *
 * @param z1 A pair representing the polar form of z1, where the first element is the magnitude and
 *           the second element is the argument (in radians).
 * @param z2 A pair representing the polar form of z2, where the first element is the magnitude and
 *           the second element is the argument (in radians).
 * @return True if the absolute value of z1 is greater than or equal to the absolute value of z2,
 *         otherwise False.
 */
fun polarGreaterEqual(z1: Pair<Double, Double>, z2: Pair<Double, Double>): Boolean {

    val (r1, theta1) = z1
    val (r2, theta2) = z2

    // Calculate the absolute values for z1 and z2
    val absZ1 = Math.abs(r1)
    val absZ2 = Math.abs(r2)

    // Check if absZ1 is greater than or equal to absZ2
    return absZ1 >= absZ2
}