Nearly impossible complex algebra problem

[Nikitin]

Homework Statement

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

Assignment 1.

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

What do I do?

Homework Equations

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?

 

[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.

 

[Mark44]

Homework Statement

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

Assignment 1. What do I do?

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?

Homework Equations

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?

 

[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!

 

[Saitama]

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.

Pranav-Arora: the solution says ±√2 - i. I duno why.

Did you try what I said?

 

[Nikitin]

a second, please

 

[Mark44]

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.

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.

Anyway I typed-in the problem into the OP

Thank you - much appreciated.

 

[Nikitin]

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

 

[Saitama]

I get x^2 + 2x -2 - y^2 -y +2yi(x+1) = 0. I have to unkowns and only one equation..

You have two equations.

Compare the real and imaginary parts on both the sides.

And check your equation again. It is wrong.

 

[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?

 

[Saitama]

OK. The new equation:

x² -2 - y² -y +2xi(y+1) = 0.

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

What do you mean with comparing both sides?

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.

 

[Nikitin]

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