Complex triangle

[Nickfytas]

Length = √(i^2+1^2)=√(1-1)=0
How is it possible the length of the hypotenuse to be 0

 

[lev888]

I don't think i is the length of the first leg.

 

[pka]

View attachment 19818

Length = √(i^2+1^2)=√(1-1)=0
How is it possible the length of the hypotenuse to be 0

Your mistake is not using ordered pairs. Complex numbers are ordered pairs.
\(1=(1,0)~\&~i=(0,1)\) now what is the distance between those.

 

[Steven G]

The vertical axis is the i-axis. Calling that distance i is like calling the horizontal distance of the triangle 1x.

If this was the regular x-y coordinate system would you say the area of the triangle is (1x)*(1y) = xy? Of course not. Same with the system you are using!

 

[HallsofIvy]

View attachment 19818

Length = √(i^2+1^2)=√(1-1)=0
How is it possible the length of the hypotenuse to be 0

It isn't! "Length" is always a positive real number, as is "distance", even in the complex plane. In particular, the length of the vertical leg, the distance from 0 to I, is 1, not i.