Differential calculus help (1 Viewer)

[Pinkled]

Hey guys, I've had 2 lectures so far for this course and decided to start working on exercises.
Could anyone please help me with this question:

If z=x+iy, express Re(z/z̅) explicitly in terms of x and y.

I understand that the complex conjugate of z is x-iy etc, but I keep ending up with an additional 2xy on the numerator.
Answer is (x^2-y^2)/(x^2+y^2).

Thanks.

 

[Carrotsticks]

Hey guys, I've had 2 lectures so far for this course and decided to start working on exercises.
Could anyone please help me with this question:

If z=x+iy, express Re(z/z̅) explicitly in terms of x and y.

I understand that the complex conjugate of z is x-iy etc, but I keep ending up with an additional 2xy on the numerator.
Answer is (x^2-y^2)/(x^2+y^2).

Thanks.

Your expression is correct, but they want the REAL part of the term. The 2xy should have an 'i' at the front, thereby making it non-real.

The whole expression is so the real part is basically that, but without the 2ixy.

 

[Pinkled]

Ah yeah, i did have an i there but i didnt know what to do with it LOL, thanks
So when it says Re, it means it only wants the real parts?

 

[Carrotsticks]

Ah yeah, i did have an i there but i didnt know what to do with it LOL, thanks
So when it says Re, it means it only wants the real parts?

Yep!

And when they say Im(...), they want the imaginary part.

So Im(2-3i) would be -3 whereas Re(2-3i) would be 2.

 

[Pinkled]

Oh, so thats what the Im is in these questions haha
Thanks for the help!