Question

PLEASE HELP ME!!
Simplify the given expression. square root of negative 49 over open parentheses 3 plus 4 I close parentheses minus open parentheses 2 minus 5 i

Answer 1

" square root of negative 49"? A negative number can not be square rooted.

Answer 2

\[\sqrt{-49}\over \left( 3+4i \right)-\left( 2-5i \right)\] @ColossalMagnitude

Answer 3

Oh, you're dealing with imaginary numbers, okay, that makes sense now. Just wait a minute and let me figure it out first, then I'll explain it to you.

Answer 4

ok thank you @ColossalMagnitude

Answer 5

Numerator would simplify to 7i because you can rewrite √-49 as √49√-1, which is equal to 7i. So, so far, we have:
\[\frac{ 7i }{ (3+4i)-(2-5i) }\]

Answer 6

We can simplify - (2 - 5i) to (-2 + 5i), so the denominator turns into:
\[\frac{ 7i }{ (3 + 4i) + (-2 + 5i) }\]

Answer 7

We can easily simplify that to:
\[\frac{ 7i }{ 9i + 1 }\]

Answer 8

how did you get from (3+4i)+(-2+5i) to (9i+1) @ColossalMagnitude

Answer 9

You can simplify (3+4i)+(-2+5i) to 3 + 4i - 2 + 5i. You know how I got 9i + 1 now?

Answer 10

quantity 7 plus 7i over 2

quantity 63 plus 7i over 82

quantity negative 7 plus 7i over 2

negative 63 plus 7 I over 82

these are the answers

Answer 11

Ummm ... wait a second, let me think for a bit.

Answer 12

ok

Answer 13

Okay, I got it. First, we want to rationalize the denominator. To do this, we would have to multiply the numerator and denominator by (9i - 1)
\[\frac{ 7i(9i - 1) }{ 9i + 1(9i-1) }\]

Answer 14

okay so far that makes sense

Answer 15

Then, we have to simplify:
\[\frac{ 7i(9i - 1) }{ -81 - 9i + 9i - 1}=\frac{ 7i(9i - 1) }{ -82 }\]

Answer 16

Make sense?

Answer 17

wouldnt you distrube the numerator

Answer 18

Not yet. But do you understand how I simplified the denominator?

Answer 19

it would be 63i-63 or am i wrong

Answer 20

oh yes i understand

Answer 21

Okay, good. Now for the numerator:
\[\frac{ 7i(9i - 1) }{ -82 } =\frac{ (7 * 9 * i^2) - 7i }{ -82 } = \frac{ (63 * -1) - 7i }{ -82 } = \frac{ -63 - 7i }{ -82 }\]

Answer 22

You can also simplify that to:
\[\frac{ -(63 + 7i) }{ -(82) } = \frac{ 63 + 7i }{ 82 }\]

Answer 23

wouldnt it be -63 + 7i?

Answer 24

You are cancelling out the negative on the numerator and the denominator, so you would just be left with what's inside the parentheses, which is (63 + 7i) / (82). So it would be this one "quantity 63 plus 7i over 82". Make sense?

Answer 25

Hello? You still there?

Answer 26

sorry im here @ColossalMagnitude

Answer 27

i understand now i wanted make sure i understoof everything

Answer 28

Okay, good, good luck with the rest of your homework/test/etc. Also, a medal would be nice if you are satisfied with my answer :).

Answer 29

lol alright thank you

Answer 30

Welcome :). Bye.