Question

[EDIT: Work down below, appreciate if anyone could look at it] What is the reciprocal of 3 - √-5?
My teacher may have skipped over this part in note-taking, so I'm at a stalemate trying to figure out what to do.

Answer 1

reciprocal of a/b is b/a
just flip the fraction
reciprocal of 2(which is same as 2/1) is 1/2

Answer 2

I figured out that part, but I accidentally missed out on the answer choices.

1) 3/2 + 3/2i
2) 3/2 - 3/2i
3) 3/4 + i√5/4
4) 3/4 - i√5/4

is there more to it than simply the reciprocal? That's what I believe

Answer 3

alright so you have to simplify that
what's the reciprocal of `3-sqrt{-5}` ??

Answer 4

1/3 - √-5

Answer 5

right \[\rm \frac{ 1 }{ 3-\sqrt{-5} }\] multiply both numerator and denominator by the conjugate

Answer 6

do you know what's conjugate ?

Answer 7

do you know what's conjugate ?

Answer 8

conjugate means change the sign, so

\[\frac{ 1 }{ 3 - \sqrt{-5} } * \frac{ 3 + \sqrt{-5} }{ 3 + \sqrt{-5} } = \frac{ 3 + \sqrt{-5} }{ 9 + 5 } = \frac{ 3 + 5i }{ 14 }\]

I feel as if I did something wrong though

Answer 9

hmm 5 would stay under the radical sign

Answer 10

\[\sqrt{-1} \rightarrow \sqrt{-1} \sqrt{5} \rightarrow i \sqrt{5}\]

Answer 11

http://imgur.com/Qp01FiP

If it's too small, let me know and I'll type it up

Answer 12

hmm

Answer 13

your work is correct.
check your answer choices are you sure its not 14 instead 4 ?