Problem

Polar coordinates are an alternative way of representing Cartesian coordinates or Complex Numbers.

A complex number  Z = x + yj

is completely determined by its real part  and imaginary part y.

Here, j is the imaginary unit.

A polar coordinate (r,θ) 

is completely determined by modulus r and phase angle θ.

If we convert complex number z to its polar coordinate, we find:

r: Distance from z to origin, i.e., √(𝑥2+𝑦2)

θ: Counter clockwise angle measured from the positive x-axis to the line segment that joins z to the origin.

Python's cmath module provides access to the mathematical functions for complex numbers.

cmath.phase

This tool returns the phase of complex number  (also known as the argument of ).

>>> phase(complex(-1.0, 0.0))
3.1415926535897931

abs

This tool returns the modulus (absolute value) of complex number .

>>> abs(complex(-1.0, 0.0))
1.0

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Task

You are given a complex . Your task is to convert it to polar coordinates.

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Input Format

A single line containing the complex number z. Note: complex() function can be used in python to convert the input as a complex number.

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Constraints

Given number is a valid complex number

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Output Format

Output two lines:

The first line should contain the value of r.

The second line should contain the value of θ.

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Sample Input

 1+2j

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Sample Output

 2.23606797749979 
 1.1071487177940904

Note: The output should be correct up to 3 decimal places.

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Solution

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from cmath import *

z = input()

print(abs(complex(z)))
print(phase(complex(z)))