How do you write the quotient (9+i) over (9-i) in standard form? I need the answer but more importantly, I need to learn how to solve these kinds of problems.

Question

Mathematics

Nicolas Ellison

25 March, 12:23

How do you write the quotient (9+i) over (9-i) in standard form? I need the answer but more importantly, I need to learn how to solve these kinds of problems.

+1

Answers (1)

Know the Answer?

Jonathan Lin · Answer 1

Since they are the conjugates of each (9-a and 9+a are conjugates, or with any number replacing 9), we multiply it by (9+i) / (9+i) to get (9+i) ^2 / (9-i^2) = (81+2i+i^2) / (9 - (-1)) = (81-1+2i) / (10) = 80/10+2i/10=8+i/5. Conjugates work because they make i into i^2 (-1) without any of the sneaky i's in the middle!