## Shuckle one year ago Write each quotient as a complex number. -2i / 1+i Is -2/-1 and +2i/-1 the correct answer?

1. zepdrix

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

2. Shuckle

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$\frac{ -2+2i^{2}}{ 1-1i+1i-1^{2}}$

3. Shuckle

Wow that thing is hard to use. -_-

4. zepdrix

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

5. Shuckle

I don't understand?

6. Shuckle

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

7. zepdrix

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

8. zepdrix

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

9. Shuckle

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

10. zepdrix

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

11. zepdrix

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

12. Shuckle

Oh.

13. zepdrix

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

14. zepdrix

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

15. Shuckle

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

16. zepdrix

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

17. Shuckle

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

18. zepdrix

ya :)

19. Shuckle

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

20. Shuckle

So the answer is -1-i?

21. zepdrix

yayyy good job \c:/

22. Shuckle

Thank you so much. :3