Fraktal

  It is easy to see that \( \mathrm{arg} \left ( \frac{a}{b} \right ) = \mathrm{arg} \left ( a \right )  - \mathrm{arg} \left ( b \right )  \) for any complex number \( a \) and \( b \). But, this is not the case for the principle value that is \( \mathrm{Arg} \) does not always equal to \( \mathrm{Arg} \left ( a \right ) - \mathrm{Arg} \left ( b \right )  \).

 Generate a computable number.

Let A be a subset of the set of all complex numbers ℂ and z 0 be an accumulation point of set A . The limit of a function f : A → ℂ as z approaches z 0 is L (denoted ) if for all 𝜀 > 0 there exists 𝛿 > 0 such that if z ∈ A and | z - z 0 | < 𝛿 then | f ( z ) - L | < 𝜀.