Question

Ignore this please...

Answer 1

ignored

Answer 2

\[\frac{5}{\sqrt{-24}} = \frac{5}{2\sqrt{6}i} = \frac{5}{2\sqrt{6}i} \times \frac{0-2\sqrt{6}i}{0-2\sqrt{6}i}\]

Answer 3

oh ok

Answer 4

Why 0 -?

Answer 5

\[\frac{5}{2\sqrt{6}i} \times \frac{0-2\sqrt{6}i}{0-2\sqrt{6}i} = \frac{-10\sqrt{6}i}{-24i^{2}}\]

Answer 6

Oh, so it can be postive.

Answer 7

0- because it's a complex conjugate

Answer 8

It's not needed, but I'm including it so you can see how it's a complex conjugate

Answer 9

ive never heard that term before

Answer 10

So any complex number can be written as\[(a+bi)\]
The conjugate of that is \[(a-bi)\]The reason they're useful is because if you multiply them by each other, you get rid of the imaginary part:\[(a+bi) \times (a-bi) = a^{2} +abi -abi -b^{2}i^{2} = a^{2}+b^{2}\]

Answer 11

oh. i remember that. i dont think we ever did anything with it though so i forgot it

Answer 12

So if you have a term where you have an imaginary number in the denominator, you can "move" the imaginary number to the denominator by multiplying the fraction by the complex conjugate divided by itself (which equals 1)

Answer 13

Can you figure out the rest from there?

Answer 14

how did they get 2sqrt 6 in the denominator if you took the sqrt out?

Answer 15

If so, vote my answer as "Best Response"

Answer 16

It simplifies like this....

Answer 17

\[\frac{-10\sqrt{6}i}{-24i^{2}} = \frac{-5\times 6^{1/2}i}{(-12) \times (-1)}\]

Answer 18

\[\frac{-5\times 6^{1/2}i}{(-12) \times (-1)} = \frac{-5i}{2 \times 6^{1} \times 6^{-1/2}} = \frac{-5i}{2\times 6^{1/2}} = \frac{-5i}{2\sqrt{6}}\]

Answer 19

Does that make sense?

Answer 20

not really. im not used to seeing it done this way

Answer 21

how did it go from -24i to -12x-1? shouldnt it be 24 and -1?

Answer 22

The numerator reduced from 10 to 5 in that step. I canceled out a 2

Answer 23

oh ok

Answer 24

So it was like \[\frac{(-1)(2)(5)\sqrt{6}i}{(-1)(2)(12)i^{2}}\] and I just canceled the 2's

Answer 25

yeah, i see that now. and you just dropped the 1/2 exponent to the bottom after?

Answer 26

Yeah, the sign of the exponent changes when you do that though.\[\frac{a^{b}}{1} = \frac{1}{a^{-b}}\]

Answer 27

ok i got it.