Why do i have to rationalize 1/(5-i) ?

Question

i don't understand... isn't rationalization only adherent to radicals?

Answer 1

Yes, all of the above answers are correct. Because most people do not like to see the i, but ok with numbers in the denominator of a fraction and the expression seems looks better to them if the i is being get rid of from the bottom and is placed on the top. And, yes, I agree that that reason cause us also to do unnecessary work.

Answer 2

Yes, but i = sqrt(-1), so it is a radical.

Answer 3

No. Most teachers don't want to see an i in the denominator either.

Get rid of it.

Answer 4

mostly because it is standard mathematical notation not to have any negative square roots in a denominator...i is the imaginary number and equals sqrt(-1)

the expression 1/(5-i) is perfectly sensible...it is common in math to rationalize as:

1/(5-i)= (5+i)/[(5-i)(5+i)]=(5+i)/[25-i^2]

=(5+i)/[25-(-1)]

=(5+i)/26

one clear advantage of writing numbers this way is that it allows you to determine the real and imaginary parts of a complex number quickly

Answer 5

i is the square root of -1

Therefore, i is a non-real radical.