What is the absolute value of 7 + 12i?

I'm thinking by "absolute value", you mean the magnitude. That is, the magnitude is the size of the vector on the complex plane. We can use the Pythagorean Theorem to calculate that. You treat the real values as your "x", and the imaginary part as your "y".

sqrt (7^2 + 12^2)

sqrt (49 + 144)

sqrt (193)