SOLUTION: What is (2 - 3i) / (1 - 4i)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: What is (2 - 3i) / (1 - 4i)      Log On


   

Question 4621: What is (2 - 3i) / (1 - 4i)
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
by this i take it you mean simplify?...if so, then multiply what you have by 1 ... is the fraction is still the same. However, my 1 is written as %28%281%2B4i%29%2F%281%2B4i%29%29

so, starting with %28%282-3i%29%2F%281-4i%29%29, we can write:

%28%282-3i%29%2F%281-4i%29%29%2A%28%281%2B4i%29%2F%281%2B4i%29%29. The reason for this is that the denominator can now be simplified into just a real number:

%28%282%2B8i-3i-12i%5E2%29%2F%281%2B4i-4i-16i%5E2%29%29
%28%282%2B5i-12i%5E2%29%2F%281-16i%5E2%29%29

since i%5E2=-1. we can write %28%282%2B5i%2B12%29%2F%281%2B16%29%29, which becomes %2814%2B5i%29%2F17

Hopefully, this is what you wanted?

jon.