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