Find roots of this function!

How would I find the roots to this particular function?

f(x) = mod((4 + x)/(4 - 3*x)) - exp(i*t)

where;

mod = modulus of the complex number
x = any complex number
exp = exponential function
i = iota
t = angle to be varied between 0 to 2pi

I need to find roots for this equation in terms of the angle (t) and plot that curve as t varies from 0 to 2pi.

Thanks.

[Matt Fig]

The MOD function takes two inputs. As you have it, the function will fail. Please re-write it so that it will work....

[Walter Roberson]

abs(x) is the complex modulus of x.

What is iota? Is that the same as the imaginary unit?