Question

Simplify

Answer 1

−1 − i

−2 − i

−1 + i

−2 + i

Answer 2

Multiply the numerator and denominator by the conjugate of -2-2i...

the conjugate of a+bi is: a-bi

Answer 3

that's right!!!!
thank youu

Answer 4

No prob :) let me know if you need more help!

Answer 5

i got 4i over 0?

Answer 6

the conjugate is -2+2i...so
\[\Large \frac{ 4 (-2+2i) }{ (-2-2i)(-2+2i) }\]

Answer 7

okay, so you multiply the numerator and the denominator by the conjugate? but you don't change the negative sign to positive

Answer 8

Which negative?
all you do is multiply both by the conjugate of -2-2i, which is -2+2i (the conjugate ONLY changes the sign of the imaginary part, not the real part)

Answer 9

i'm doing something wrong here... ://

Answer 10

the negative 2

Answer 11

do i distribute 4 into -2 + 2i?

Answer 12

Yes, simplify the numerator and denominator both

Answer 13

i got 6 for the numerator..?

Answer 14

and -4..? eek

Answer 15

Their should be an i... show your work.

Answer 16

The denominator should be real, the numerator should have an i.

Answer 17

so -8 + 2 (-1)
i=(-1)
as the numerator

Answer 18

\[\Large \frac{ 4 (-2+2i) }{ (-2-2i)(-2+2i) } =\frac{-8+8i }{ (-2-2i)(-2+2i) }\]

Answer 19

i is the square root of -1. i is not -1.

Answer 20

got it. so how would you deal with the denominator

Answer 21

FOIL it/distribute it.

Answer 22

Same way you would with something like (x-2)(x+2). Remember that i*i = -1 (i^2 = -1)

Answer 23

so...
4 + 2 -4i + 4i -4i

Answer 24

whoops...! i mean 4 + 4i + 4i - 4i

Answer 25

That doesn't look right...

\[\Large \frac{-8+8i }{ (-2-2i)(-2+2i) } = \frac{-8+8i }{4+4i-4i+4i^2 }\]

Answer 26

crap.

Answer 27

so then it would be..
-8 +8i / 4 + 4i

Answer 28

no, you're almost there... i^2 is -1.

Answer 29

i mean i!!!

Answer 30

so... -16/0 ?!?!?!

Answer 31

Oh wait, it was, i made a mistake \[\Large \frac{-8+8i }{ (-2-2i)(-2+2i) } = \frac{-8+8i }{4+4i-4i-4i^2 }\]

Answer 32

But how did you get -16... your i's keep disappearing...

Answer 33

noo! how do i simplify that without multiplying each side by i, to get i^2 to then be -1..?

Answer 34

i^2 is equal to -1.

Answer 35

we have this. which we can simplify \[\Large \frac{-8+8i }{4+4i-4i-4i^2 }\] to \[\Large \frac{-8+8i }{4-4i^2 }\] and once more to \[\Large \frac{-8+8i }{4-4(-1) }\]

Answer 36

thank you so much for taking the time to help me :) i'm so sorry my i's keep disappearing ://

Answer 37

Think of them as x's. They can't just disappear, unless it's an i^2 which is -1.

Answer 38

got it! thank youu! so how about this...
-8 + 8i / 8

Answer 39

Excellent! :) now you can still simplify a bit more...

Answer 40

ahhhh :// i don't know what to do!!

Answer 41

Yes you do :P

Answer 42

multiply each side by 8? then it would be -64 +8i ?

Answer 43

that seems odd...hmm

Answer 44

No you just need to simplify... \[\Large \frac{ -8 + 8i }{ 8 } =\frac{ -8 }{ 8 }+\frac{ 8i }{ 8 }\]

Answer 45

okay. alright. so 0i/8 ?

Answer 46

i'm so lost :// so sorry

Answer 47

Just simplify each of those one at a time. What's -8/8? What's 8i/8?

Answer 48

-1 + 1i ?

Answer 49

Excellent :)

Answer 50

AHHHHH! thank you so so so so so SO much!!

Answer 51

haha you're welcome

Answer 52

i wish i could give you a million medals!!

Answer 53

:D