complex.org

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Complex numbers; getting started

Rabbit holes

These are rabbit holes about complex numbers

⌜🐇 Rabbit holes to get started with CIMMIC are:

1. This would be a good text-based starter for complex numbers. (R_C-hole)
2. This is Eddie Woo’s excellent series of YouTube videos on complex numbers. (R_C-hole)
3. This is the Wikipedia article. (R_O-hole)
4. (R_O-hole)
5. (R_FYI-hole)

🐇⌟

Complex numbers

• cite:&larson2007precalculus

import Data.Complex

x = 0 :+ 3

x

0 :+ 3

realPart x

0.0

imagPart x

3.0

y = 1 + x

let z = y ^ 2

a = 0 :+ 1

a ^ 1

0.0 :+ 1.0

a ^ 2

(-1.0) :+ 0.0

[(0 :+ 1)^x | x <- [0..15]]

[1.0 :+ 0.0,0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0),1.0 :+ (-0.0),0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0),1.0 :+ (-0.0),0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0),1.0 :+ (-0.0),0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0)]

:{
complxPower nx | null nx = []
complxPower (n:nx) = (0 :+ 1)^n : complxPower nx               
:}

complxPower [0..15]

[1.0 :+ 0.0,0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0),1.0 :+ (-0.0),0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0),1.0 :+ (-0.0),0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0),1.0 :+ (-0.0),0.0 :+ 1.0,(-1.0) :+ 0.0,(-0.0) :+ (-1.0)]

We can try to make this print prettier

import Numeric

showFFloat (Just 0) (-5.014) ""

-5

:{
complxPower2 nx | null nx = []
complxPower2 (n:nx) = ri : complxPower2 nx
  where ri = let ccalc = ((0 :+ 1)^n)
             in if (realPart ccalc) /= 0
                then (showFFloat (Just 0) (realPart ccalc) "")
                else "i"      
:}

complxPower2 [0..10]

["1","i","-1","i","1","i","-1","i","1","i","-1"]

or just

:{
complxPower6 nx | null nx = []
complxPower6 (n:nx) =
  let
    ccalc = ((0 :+ 1)^n)
    ri =
      if (realPart ccalc) /= 0
      then (showFFloat (Just 0) (realPart ccalc) "")
      else "i"
   in ri : complxPower6 nx
:}

Footnotes

[fn:1] Cardinality of a set is simply the number count of elements therein.