Complex Rectangular Triangle Hypotenuse

[SKG_Scintill]

This is something that bothered me in high school. After graduation I thankfully forgot about it. But ever since SlayerApocalypse666 asked me to do some simple math, my mind went mathematical berserk, resulting in me hitting the wall I hit in the past.

The idea is that you have a rectangular triangle, one leg on a real axis, the other on an imaginary axis. The real leg has a length of 5, the imaginary leg has a length of 4i.

a^2 + b^2 = c^2 (olol duh)
25 - 16 = c^2
c^2 = 9
c = 3

The hypotenuse is shorter than the real leg, but it still has a real length. It can be measured, it is there, the point in which it makes an angle with the imaginary leg also exists.
As long as the real leg stays longer than the imaginary leg, the hypotenuse will be a real number.

But what about when they are equal? legs being 5 and 5i respectively...
The hypotenuse is 0.
The maths behind it don't bother me, but the fact that the distance is to be drawn on a sheet of paper.

Now, the same way that a square is the distance of a line drawn behind that same line (staying in a 1-dimensional space obviously) and a cube is the distance of a square drawn behind that square (in a 2-dimension space), you can draw the real leg with length 5, extend a line from an end in that line segment into a theoretical 4-dimensional space and have a measurable hypotenuse of 0.
But when you try to do that with the triangles that have a measurable hypotenuse with a length > 0, the hypotenuse would have to rotate around the real leg (still reasonable theoretically due to the angle being imaginary as well).

tan ∠A = 4i/5
∠A = arctan(4i/5) ≈ 38.67i deg

My question (finally): Following what curve (formula if it's possible) does the hypotenuse extend from the real leg (length of 5) for all lengths < 5i for the imaginary leg?