Question

Write each quotient as a complex number.
-2i / 1+i

Is -2/-1 and +2i/-1 the correct answer?

Answer 1

\[\large\rm \frac{-2i}{1+i}\left(\frac{1-i}{1-i}\right)=\frac{-2i-2}{2}\]Hmm, do you understand this step that I applied?

Answer 2

Yes, I understand that you have to multiply the numerator and denominator by the complex conjugate of the denominator.
But from doing that I got the numbers\[\frac{ -2+2i^{2}}{ 1-1i+1i-1^{2}}\]

Answer 3

Wow that thing is hard to use. -_-

Answer 4

Woops your denominator is \(\large\rm 1-1i+1i-i^2\)

Answer 5

I don't understand?

Answer 6

Oh I see, the one is an i. But I still don't know what the final solution should be?

Answer 7

So the middle terms cancel out in the denom, ya? :)\[\large\rm \frac{ -2+2i^{2}}{ 1-1i+1i-i^{2}}=\frac{ -2+2i^{2}}{ 1-i^{2}}\]

Answer 8

i^2 is -1, so the negatives give us a +1 in that spot

Answer 9

Yes, and then multiplied to the denominator of +1 give you a negative one on the bottom?

Answer 10

\[\large\rm =\frac{ -2+2(-1)}{ 1-(-1)}\]

Answer 11

No you're not multiplying, you're adding down there.

Answer 12

Oh.

Answer 13

Oh woops that's a 2i for the first term in the numerator :O

Answer 14

\[\large\rm =\frac{ -2i+2(-1)}{ 1-(-1)}\]

Answer 15

So after that it should be -2i -2 over 1?

Answer 16

No, your denominator simplifies to this:\[\large\rm =\frac{ -2i+2(-1)}{ 1+1}\]

Answer 17

because (-1)(-) makes a positive one, right?

Answer 18

ya :)

Answer 19

So then, it'd be -2+2i over 1+1 which will equal -2 +2i over 2, and then I should divide?

Answer 20

So the answer is -1-i?

Answer 21

yayyy good job \c:/

Answer 22

Thank you so much. :3