Question

Simplify...

Answer 1

\[\huge\sqrt{-6}(2+\sqrt{-8})\]

Answer 2

multiply each term in braces with root9-6)
next use formula root(a)root(b)=root(a*b)

Answer 3

this has to do with imaginary numbers...

Answer 4

2root(-6)+root(48)
use root(-1)=i
hint write 48 as 16*3

Answer 5

\[\huge 2i \sqrt{6} + 4i \sqrt{3}?\]

Answer 6

there will be no i in 2nd term check once

Answer 7

oh right\[\huge 2i \sqrt{6}-4\sqrt{3}\]

Answer 8

i still dont get it ..look at this:

Answer 9

slight mistake in 2nd term root(48)=root(16*3)=4 root(3)

Answer 10

the first term cannot have an i because its not one of the choices...look at the attachement

Answer 11

@yummydum, you can change the order how you write it

\[\huge -4 \sqrt{3}+2i\sqrt{6} \]

Answer 12

it is answer D u got it just see

Answer 13

@Spacelimbus look at the attachment...

Answer 14

oh :|

Answer 15

that's what I did.

Answer 16

\[ a-b = -b+a \]

Answer 17

I dont get this one...

Answer 18

what would you do first?

Answer 19

@Calcmathlete

Answer 20

im not sure :\

Answer 21

First simplify the denominator...

Answer 22

simplifying the denominator will already help you a lot, because they are equal terms.

Answer 23

okay ill give it a try

Answer 24

denominator = 1-i ??

Answer 25

oh wait

Answer 26

not quite.

Answer 27

1+9i

Answer 28

Distribute the negative.

Answer 29

\[1+9i\]

Answer 30

now what??

Answer 31

its just\[{7i}\over{1+9i}\]now :S

Answer 32

@Spacelimbus You have to do operations before you bring out i right?

Answer 33

well, the denominator is a real number, the only way to get a complex number into a real number is by multiplying it with it's complex conjugate.

\[ (x+iy)(x-iy)=x^2+y^2 \] always real, always positive.

Answer 34

So in this case, expand the quotient with the complex conjugate.

Answer 35

^what does that mean i do?

Answer 36

Do you know what a conjugate means?

Answer 37

yes

Answer 38

so the conjugate of 1+9i?

Answer 39

\[7i~(1-9i)\over1+9i~(1-9i)\]\[7i-63i \over1+81\]

Answer 40

63i^2

Answer 41

well done.

Answer 42

so thats:\[7i+63\over82\]

Answer 43

right?

Answer 44

looks correct to me