# Real and imaginary numbers

• Apr 29th 2010, 06:03 AM
zizou1089
Real and imaginary numbers
I am having trouble with Q5 in the attached file,

For part (a) after expanding and simplifying I have the answer:

f(z)=(36x^2)+4iBy-12ix

How would I wite the real and imaginary parts of the function in terms of B, x and y?

Also for which values of B is f differentiable? and where?....

...... Btw is there a program of some sort I can download to write up the questions in a more 'mathematical way' so I can write the symbols, instead of attaching the files?? Thanks
• Apr 29th 2010, 07:03 AM
HallsofIvy
Quote:

Originally Posted by zizou1089
I am having trouble with Q5 in the attached file,

For part (a) after expanding and simplifying I have the answer:

f(z)=(36x^2)+4iBy-12ix

How would I wite the real and imaginary parts of the function in terms of B, x and y?

Since x, y, and $\displaystyle \beta$ are real, that is just $\displaystyle (36x^2)+ (4\beta y- 12x)i$. The "real part" is $\displaystyle 36x^2$ and the imaginary part is $\displaystyle 4\beta y- 12x$

Quote:

Also for which values of B is f differentiable? and where?....
I assume you mean "differentiable with respect to z". The function f(z)= g(x,y)+ h(x,y)i is differentiable with respect to z= x+ iy only if it satisfies the "Cauchy-Riemann equations":
$\displaystyle \frac{\partial g}{\partial x}= \frac{\partial h}{\partial y}$ and
$\displaystyle \frac{\partial g}{\partial y}= -\frac{\partial h}{\partial x}$

Quote:

...... Btw is there a program of some sort I can download to write up the questions in a more 'mathematical way' so I can write the symbols, instead of attaching the files?? Thanks
There is a LaTex equation editor at Online LaTeX Equation Editor
You don't need to download, it just open a new tab page (in internet Explorer) and go to that site.

Type your equation in the box, selecting "special" symbols from the menu, then copy and paste the result. That's what I did here:
$\displaystyle \int_{-\infty }^{\infty }e^{-x^{2}}dx$
If you move your cursor over that, you will see the code needed for that.
Different web-sites use different HTML markers to begin end LaTex. On this site, you need to begin with "[math ]" and end with [/math ]" (without the space I put in so they would not be interpreted as LaTex and you could see them).

But I really prefer just to type in the LaTex myself. There is a tutorial on this site at http://www.mathhelpforum.com/math-help/latex-help/.
• Apr 29th 2010, 03:31 PM
zizou1089
Thanks alot for the help