#!/usr/local/bin/perl

# ----------------------------------------------------------------
# John Kerl
# kerl.john.r@gmail.com
# 2005-01-11
#
# This converts complex numbers from rectangular (real-imaginary) coordinates
# to polar (magnitude-phase) coordinates.  Example:
#
# bash$ cat a.txt 
#      0  0
#      1  0
#      0  1
#     -1  0
#      0 -1
#      1  1
#      1  2
#      1  3
# bash$ prect2polar a.txt
#      0.00000000000      0.00000000000
#      1.00000000000      0.00000000000
#      1.00000000000      1.57079632679
#      1.00000000000      3.14159265359
#      1.00000000000     -1.57079632679
#      1.41421356237      0.78539816340
#      2.23606797750      1.10714871779
#      3.16227766017      1.24904577240
# ----------------------------------------------------------------

$lineno = 0;
while ($line = <>) {
	chomp $line;
	$lineno++;
	$line =~ s/^\s+//;
	$line =~ s/\s+$//;
	my @fields = split /\s+/, $line;
	if (@fields == 2) {
		$re = $fields[0];
		$im = $fields[1];
	}
	elsif (@fields == 1) {
		$re = $fields[0];
		$im = 0.0;
	}
	else {
		die "$0:  unrecognizable input at line $lineno.\n";
	}
	$mag = sqrt($re * $re + $im * $im);
	$phz = atan2($im, $re);
	printf "%18.11f %18.11f\n", $mag, $phz;
}