Question

What is the meaning of absolute value of a complex number?

Answer 1

The "absolute-value" or "modulus" of a complex number is the distance between that point and the origin.

So, in our example from before, the absolute-value of 5 - 12i is 13.
So if you plot the point 5-12i on the complex plane (it is in the 4th quadrant), the distance from 5-12i and the origin is 13. Which makes sense fro many angles. Either via the "distance formula" or Pythagorean Theorem (it will form a 5-12-13 right triangle).

Answer 2

And that's in accordance to what the absolute-value of -7 is. It is the distance from -7 to the number 0 on the number line. It is 7 spaces away, therefore, abs(-7) = 7.
So absolute-value always represents "distance".

Answer 3

Thank you so much

Answer 4

Welcome.