# Nearly impossible complex algebra problem

1. May 31, 2013

### Nikitin

1. The problem statement, all variables and given/known data
https://wiki.math.ntnu.no/lib/exe/fetch.php?hash=d26b1f&media=http%3A%2F%2Fwww.math.ntnu.no%2Femner%2FTMA4115%2F2012v%2Fexams%2Fkont.eng.pdf [Broken]

Assignment 1.

"Find all complex numbers s such that Im(-z + i)= (z+i)2"

What do I do?

2. Relevant equations

3. The attempt at a solution

I got to Im(-z) + 1 = z2+2zi -1 => Im(-z) = (z-1+i)(z+1+i).

But I have no idea what to do next... Or if I even have done anything useful so far.

Help?

Last edited by a moderator: May 6, 2017
2. May 31, 2013

### Saitama

I can't see any other way than substituting z=x+iy. Try that, it is easy to solve. There might be some other method too.

3. May 31, 2013

### Staff: Mentor

Instead of posting a link to a PDF, why not just enter the text of the problem here? Some members figure that if the OP isn't willing to take the time to provide the problem statement, why should they bother?

Last edited by a moderator: May 6, 2017
4. May 31, 2013

### Nikitin

I did not mean it like that - I simply can't do latex and thus it's easier to present the problem that way. I apologize if you got offended by the OP or by the title. Anyway I typed-in the problem into the OP

Pranav-Arora: OK, thanks!

5. May 31, 2013

### Saitama

Did you try what I said?

6. May 31, 2013

### Nikitin

7. May 31, 2013

### Staff: Mentor

No, I wasn't offended by your post or the title. It takes a lot more than that to offend me. It's just that it's much more convenient for readers if the problem statement is right here, not off on some other web site.

For many problems, including this one, you don't need LaTeX. There are some controls build into this site (click the Go Advanced button under the entry pane to see them). The only "mathematical" things you needed for this problem are exponents, which you can do by clicking the X2 button in the advanced menu that appears after you click Go Advanced.
Thank you - much appreciated.

8. May 31, 2013

### Nikitin

Pranaev: I get x2 -2 - y2 -y +2xi(y+1) = 0. I have to unkowns and only one equation..

Last edited: May 31, 2013
9. May 31, 2013

### Saitama

You have two equations.

Compare the real and imaginary parts on both the sides.

And check your equation again. It is wrong.

10. May 31, 2013

### Nikitin

OK. The new equation:

x2 -2 - y2 -y +2xi(y+1) = 0.

What do you mean with comparing both sides? x = Re(z) and y = Im(z), but how does that help me?

11. May 31, 2013

### Saitama

Nope, still wrong. Show your steps so that we can point out the error.

For example, you have something like a+ib=3+2i, you can compare the real and imaginary parts on both sides and get a=3 and b=2. Similarly, you have 0+0i on RHS in this case.

12. May 31, 2013

### Nikitin

I used the 0 + 0i trick to get the correct answer. Thanks :)