SOLUTION: I do not know how to begin this problem. 4/(2-3i) + 2/(1+i) [4 divided by (2-3i)]+[2 divided by (1+i)] I have the correct answer I just need to know the process to get the

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I do not know how to begin this problem. 4/(2-3i) + 2/(1+i) [4 divided by (2-3i)]+[2 divided by (1+i)] I have the correct answer I just need to know the process to get the       Log On


   

Question 711561: I do not know how to begin this problem.
4/(2-3i) + 2/(1+i)
[4 divided by (2-3i)]+[2 divided by (1+i)]
I have the correct answer I just need to know the process to get the answer. (21/13 - 1/13 i)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
You do the same as you have learned already. Two fractions as a sum, different denominators, find lowest common denominator; change the fractions to equivalent forms using the common denominator.


4%2F%282-3i%29++%2B+++2%2F%281%2Bi%29
Lowest common denominator is %282-3i%29%281%2Bi%29



%284%281%2Bi%29+%2B+2%282-3i%29%29%2F%28%282-3i%29%281%2Bi%29%29
%284%2B3i%2B4-6i%29%2F%28%282-3i%29%281%2Bi%29%29
%288-3i%29%2F%28%282-3i%29%281%2Bi%29%29

Not finished. You still want to do something about those complex numbers as the denominator. Multiply numberator and denominator by the conjugate of each of the complex numbers in the denominator and then continue simplifying.



Let's look JUST at the denominator:
%282-3i%29%281%2Bi%29%282%2B3i%29%281-i%29
=%282-3i%29%282%2B3i%29%281%2Bi%29%281-i%29
=%284%2B9%29%281%2B1%29
=13%2A1
=13

The multiplying and simplifying in the numerator is left for you to do (which is to multiply the three complex numbers of the numerator).