Last Updated: 18 Apr, 2021
Multiplying Complex Numbers
Easy
Asked in companies
You are given two complex numbers 'NUM1' and 'NUM2' as strings, “A+Bi” where ‘A’ represents the real part and ‘B’ represents the imaginary part.
You have to find the complex multiplication of given numbers and return it as a string “A+Bi”, where ‘A’ represents the real part of the result and ‘B’ represents the imaginary part of the result.
Input Format:
The first line contains a single integer ‘T’ representing the number of test cases.
The first line of each test case will contain a single string, representing the first complex number 'NUM1'.
The second line of each test case will contain a single string, representing the second complex number 'NUM2'.
Output Format:
For each test case, return the complex multiplication as a string of the form “A+Bi”.
Note:
You don’t need to print anything; it has already been taken care of. Just implement the given function.
Constraints:
1 <= T <= 10^5
-10^7 <= A, B <= 10^7
Time Limit: 1 sec
Approaches
Let first and the second complex number be, ‘a + bi’ and ‘c+di’, then
'RESULT' = (a + bi) *(c + di) = (ac + adi) = (bci + bd * (-1)) as i^2 = -1
‘RESULT’ = (ac - bd) + (ad+ bc) i
The steps are as follows:
- We will parse the input and extract the real and imaginary parts of the number.
- Let ‘REAL1’, ‘IMG1’ store the real and imaginary part of the first number.
- Let ‘REAL2’, ‘IMG2’ store the real and the imaginary part of the second number.
- 'REAL_RESULT', 'IMG_RESULT' will store the real part and the imaginary part of the result.
- 'REAL_RESULT'= ‘REAL1’ * ‘REAL2’ - ‘IMG1’ * ’IMG2’
- 'IMG_RESULT' = ‘REAL1’ * ‘IMG2’ + ‘REAL2’ * ‘IMG1’
- 'RESULT' = 'REAL_RESULT' + ‘+’ + 'IMG_RESULT' + ‘i’
- Return 'RESULT'.