- #1
sjmacewan
- 35
- 0
Hello there,
I've been given the task of find the real part for the following expression
[tex]\sqrt{x+iy}[/tex]
And I'm a bit stuck. I figure that I'll just say that that equation is equal to some other imaginary number a+bi where 'a' is the real part and 'b' is the imaginary part, and try to solve for a. But after squaring both sides i get stuck immediately...
[tex]x+iy = a^2 + 2abi - b^2[/tex]
And i don't know where to go. Perhaps I'm going the wrong way with this one, any help would be appreciated.
Edit: Ok, I've made some progress...
I know then that
[tex]x = a^2 - b^2[/tex]
and
[tex]iy = 2abi[/tex]
So i try to get rid of the b term in the real one, but the only substitution I can make results in a y term being introduced into the real part, which is just adding another imaginary number in there...
I've been given the task of find the real part for the following expression
[tex]\sqrt{x+iy}[/tex]
And I'm a bit stuck. I figure that I'll just say that that equation is equal to some other imaginary number a+bi where 'a' is the real part and 'b' is the imaginary part, and try to solve for a. But after squaring both sides i get stuck immediately...
[tex]x+iy = a^2 + 2abi - b^2[/tex]
And i don't know where to go. Perhaps I'm going the wrong way with this one, any help would be appreciated.
Edit: Ok, I've made some progress...
I know then that
[tex]x = a^2 - b^2[/tex]
and
[tex]iy = 2abi[/tex]
So i try to get rid of the b term in the real one, but the only substitution I can make results in a y term being introduced into the real part, which is just adding another imaginary number in there...
Last edited: