Question

How do you find the absolute value of the complex number?

Answer 1

If `z = a+ib` where `a, b in RR` then `|z| = |a+ib| = sqrt(a^2+b^2)`

To picture this, think of `a+ib` as a point `(a, b)` in the plane.
The modulus is the distance of that point from the origin `(0,0)`.

We can calculate the distance by dropping a perpendicular onto the real axis at `(a, 0)` and using the Pythagorean Theorem on the right angled triangle formed by these three points, which has sides of length `a`, `b` and `sqrt(a^2+b^2)`.