1. ## Question from a non-math-head

I'm a photographer; I need to incorporate a "complex" math formula into a picture I'm creating and found the following at Math.com under "Complex Definitions of Functions and Operations" :

tan(a + BI) = ( tan(a) + i tanh(b) ) / ( 1 - i tan(a) tanh(b))
= ( sech 2(b)tan(a) + sec 2(a)tanh(b) i ) / (1 + tan 2(a)tanh 2(b))

Rather than making an error in using something that makes little sense, I thought I'd ask here. I'm seeking something about that long. BTW, this is for a personal project about the level of awareness of math in children.

Thanks, Ken

2. Can you use something a bit more standard?
$\sin(a+bi)=\sin(a)\cosh(b)+i~\cos(a)\sinh(b)$

3. Say, thanks for the reply. I don't see why not, however, my curiosity begs the question:
what's wrong with the equation I found? Are you suggesting that mere mortals might have a better grasp of what you sent? On that note, I'd say it would make no difference.
Perhaps if I attach what I've created, you'll see what I mean:

4. There is nothing wrong with it.
I just think that using something familiar to more people would be best.
If you want a longer image here is another:
$z = a + bi\, \Rightarrow \,\cos (z) = \dfrac{{e^{iz} + e^{ - iz} }}
{2} = \cos (a)\cosh (b) - i\,\sin (a)\sinh (b)$

5. I just copied it over and will get to it tomorrow. It's appreciated. BTW, what does it reference? I more or less like to know what I'm doing!

6. It called writing an elementary complex valued function in the $u+i\,v$ form.

7. Thanks, AND...I'm having a helluva time trying to write it out...can't figure how to have the squared iz's appear where they're supposed to and the numerator/denominator as well. It really needs to be imported in a higher res than I can get off the forum site page or I'll try a few fonts and other tricks but it may be a lost cause. More simply put it may not worth the trouble since you've acknowledged the formula I've got is not too bad. Again, I do appreciate the assistance. Ken