What's wrong with it is that "distance" is a positive real number (have you ever seen a meter stick or ruler with "i" on it). In order to get that we define the absolute value of a complex number as

where

is the "complex conjugate" of z. In particular, the complex conjugate of i is -i so that

.

I don't understand what you are trying to say here. What does "i unit= 3"

**mean**? It sounds like you are just trying to

**redefine** "i" to be "3i". You can't do that and have the same number system as before. If you start with "non-sense", labeling "3" as a "1", leads to non-sense: |3|= 1!

(This reminds me of a joke Abraham Lincoln used to tell: Question: if you call a lambs tail a leg, how many legs does it have? Answer: four-

**calling** a tail a leg doesn't

**make** it one! In mathematics we are pretty free to "call" things what we want. But once you have labled a point on the y axis "3" you cannot then also label it "i".)