Question

Express each number in terms of i.

1. √-32
2. 2√ -18
3. √ -1/9

Answer 1

Hey what do you think we do first?

Answer 2

Uh, i really am not sure

Answer 3

Well "i" is another term for -1

so we have \[\sqrt{-32}\]

what do you think we do with the i?

Answer 4

Multiply it with √ -32?

Answer 5

Yes so when we do that, it become postive but first, what do we do with the 32?

Answer 6

simplify?

Answer 7

Yes so what do we get?

Answer 8

uhm not sure how to do that, i forgot

Answer 9

Well to do that we need to find 2 numbers that multiply to get 32 BUT one of them has to be able to be sqrt.

Answer 10

8 and 4

Answer 11

Great, can we simplify more?

Answer 12

wait no

Answer 13

we need one number of the 2 that can be sqrt

Answer 14

For example, lets say we have \[\sqrt{18}\]

6,3,9,2 go into it.

But only one of them can be sqrt which is 9
\[\sqrt{9}=3\]
so we are left with \[3\sqrt{2}\]

Answer 15

Do you get it?

Answer 16

so it's √ 16 for 32 right?

Answer 17

COrrect and sqrt16 is?

Answer 18

4

Answer 19

so now 4 have been sqrt so we only have 2 left and that stays under the sqrt.

And we bring the "i" outside so what would i answer be?

Answer 20

Wait what do you mean we have 2 left,

Answer 21

we had 16*2 and we only can sqrt 16 so 2 stays

Answer 22

16*2=32

Answer 23

ohh i see now

Answer 24

So it's 4√ 2

Answer 25

you forgot the i D:

Answer 26

oh lol 4i√ 2

Answer 27

Correct :D

Answer 28

Ok #2

what would we get?

Answer 29

3i√ 2

Answer 30

Then would it be 2x3i√ 2

Answer 31

Yes so whats 3*2 i

Answer 32

6i√ 2

Answer 33

Correct :D

#3?

Answer 34

oh uhm not sure how to do this one

Answer 35

what is 9sqrt?

Answer 36

3

Answer 37

what is -1(-1)

Answer 38

1

Answer 39

remember -1 is "I" so its i so we have for the answer?

Answer 40

1/3i

Answer 41

no -1(i) ?

Answer 42

oh -1(i) is -1(-1) which is 1?

Answer 43

-3(i) = 3i so -1(i) = i

Answer 44

ohh okay

Answer 45

So \[\frac{ i }{ 3 }\]

Answer 46

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Answer 47

Thanks so much !

Answer 48

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Answer 49

Oh really? Is it an only pay once thing?

Answer 50

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Answer 51

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Answer 52

Hm I'll look into it, thank you so much!

Answer 53

Yes anytime :D

Answer 54

Hm I'll look into it, thank you so much!