HackerRank Python Solution - Math Topic - Polar Coordinates

• 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 x and imaginary part y. Here, j is the imaginary unit. 

• A polar coordinate (r,φ) is completely determined by modulus r and phase angle φ.

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

• r: Distance from to origin, i.e., √ (x^2 + y^2)

• φ: Counterclockwise 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 the complex number z (also known as the argument of z).

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

3.1415926535897931

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

 

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

1.0

Task: 

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

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. 

Constraints:

Given number is a valid complex number.

Output Format: 

• Output two lines: 
• The first line should contain the value of r.
• The second line should contain the value of φ.

Sample Input:

1+2j

Sample Output:

 2.23606797749979 

 1.1071487177940904

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

Solution:

import cmath

ip = complex(input())

print(abs(ip))

print(cmath.phase(ip))

//or use polar()

print(*cmath.polar(complex(input())), sep='\n')

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