Has anyone noticed the funny things that happen when you try to express i as real? For instance, when you ask for the abs of i, it returns 1. If you try this: abs(2+i)², it returns the square root of 5.
Has anyone noticed the funny questions that are asked when the relevant articles don't get read? ;)
abs( is the complex modulus. It measures the absolute distance between the origin and the points represented by the numbers in the brackets when they are plotted in the complex plane; abs(2+i) equals √(2²+1²).
An interesting note is that the formula abs(x)=√(real(x)2+imag(x)2) applies to both reals and complex.
For reals, you use absolute values in order to simplify square roots, henceforth it is logical to go backwards when taking the absolute value of a number.
Rule: When factoring out a variable from a radical, if the index is even and the new power is odd, absolute values must be applied.
√(x2) ≠ x
√(x2) = |x|