What is the absolute error for complex values? I know that in real numbers, if we want to find the absolute error between two real values, let be $a_1$ and $a_2$, we use the formula $|a_1-a_2|$.
But if I have two complex values, $z_1=x_1+iy_1$ and $z_2=x_2+iy_2$, how can I find the absolute error between them?
Have I use the same formula that is used with real values?
Waiting for help, please.
Edit:
I'm working on my master thesis. I have a PDE with complex values and I have to solve it numerically.
So I want to compute the absolute error between the approximate value that I got and the exact value.
 A: If you just want to generalize the real case, you can just use the complex absolute value: For a complex number $z \in\mathbb{C}$ with $z=x+iy$ (here $x,y\in\mathbb{R}$), its absolute value is defined via
$$|z| := \sqrt{x^2+y^2 }= \sqrt{z\cdot\bar z},$$
where $\bar z = x-iy$ denotes the complex conjugate to $z$.
So given two complex numbers $z_1,z_2$, their (euclidian) distance can be defined as
$$|z_1-z_2| = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}.$$
A: Absolute error is the quantity's measured value minus its actual value.
This is in opposition to relative error, which is the ratio of the absolute error to the absolute value of the quantity's actual value. (The absolute value of the denominator is taken so that the sign of the relative error reflects the direction of the error.)
Although the adjective "absolute" in absolute error does not mean absolute value, it is nevertheless not uncommon to drop any negative sign when making these ‘error’ computations.
Hence, the answer to your question, according to your requirement, is $$|z_1-z_2|,$$ that is, the absolute value (modulus) of the difference between the two complex (or real) values.
