Question

simplify the expression using the imaginary unit i:
2√-24 + 6
simplify the expression:
(2-3i)/(1+5i)
please help and walk me through the steps!

Answer 1

hint:\[i^2 = -1\]

Answer 2

\[2\sqrt{-1.24} + 6\]

Answer 3

still confused?

Answer 4

do i distribute the 2 and then add 6 or is that not important?

Answer 5

no. you can put i^2 instead of -1\[2\sqrt{i^224} + 6\]

Answer 6

get it?

Answer 7

i is the imaginary unit here.okay?

Answer 8

yes

Answer 9

so we can say\[2\sqrt{i^2}\sqrt{24}+ 6\]

Answer 10

look at my previous one if you don't understand last one

Answer 11

I think you still have problems.. right?

Answer 12

im just taking a while to respond because i'm trying to understand it better

Answer 13

okay. that's fine. do you know why we use this i^2 thing here?

Answer 14

no not really, sorry

Answer 15

because you can't solve \[\sqrt{-24}\]

Answer 16

you can't square root negative numbers.

Answer 17

ohhh, that makes sense, so what it's trying to do is make it positive then

Answer 18

yes. so we get rid of negative part using i^2.

we say \[i^2 = -1\]

Answer 19

okay i see so it turns into positive 24 and then we square root it

Answer 20

\[\sqrt{-24} = \sqrt{-1.24} = \sqrt{i^224} = \sqrt{i^2}\sqrt{24}\]

Answer 21

\[\sqrt{i^2}\sqrt{24} = i\sqrt{24}\]

Answer 22

okay?

Answer 23

okay i think i understand it a little better

Answer 24

yes. now you can do further simplifying
\[i\sqrt{24} = i\sqrt{2^2.6}\]

Answer 25

that means \[2i\sqrt{6}\]

Answer 26

so \[2\sqrt{-24} + 6 = 2i\sqrt{6} + 6\]

Answer 27

and \[2\sqrt{-24} + 6 = 2i\sqrt{6} + \sqrt{6}\sqrt{6}\]

Answer 28

oh wow thank you so much, i was stuck on that question for an hour...

Answer 29

and I did a mistake:)
\[2\sqrt{-24} + 6 = \sqrt{6}(4i + \sqrt{6})\]

Answer 30

do it it again. you should get my last answer.

Answer 31

what about 2nd one?

Answer 32

i'm not exactly sure how to do it it's confusing me a lot

Answer 33

you want to get removed 'i' part from denominator.

Answer 34

denominator is (1 + 5i)

Answer 35

okay, and i do that by adding to both sides?? or am i incorrect

Answer 36

yes. you don't add things in fractions. you can't do that.

Answer 37

you need to multiply both sides by (1-5i)

Answer 38

\[\frac{(2-3i)(1-5i)}{(1+5i)(1-5i)}\]

Answer 39

okay, and sorry that's what i meant i'm just a little stressed out
so its:
(2-3i)*(1+5i)
_____________
(1 + 5i) (1 + 5i)

Answer 40

whoops

Answer 41

it is not (1+5i). it should be (1-5i)

Answer 42

http://i.ytimg.com/vi/deUghb0U9Ds/maxresdefault.jpg

Answer 43

oh okay! that makes a lot of sense

Answer 44

yeah. conjugate. you want to multiply by conjugate of (1+5i)

Answer 45

can you do it now?

Answer 46

yes, thank you so much

Answer 47

you are welcome:)