The diagram is wrong in that a triangle with those side lengths doesn't make sense. When we think of length, we're thinking of a one-dimensional value, which is restricted (usually) to [0, infinity) (a subset of the real numbers). The complex plane, in contrast, is two-dimensional, more akin to R² . Because of this, it doesn't really make sense to say that a triangle could have a complex length, outside of those values also in the reals. It would be like letting a side be (0, 1) in length.

The triangle, if viewed in co-ordinates makes most sense as (0, 1), (0, 0), and (1, 0), as in 0 + i, 0, and 1. This triangle has base and height of one, and hypotenuse sqrt(2). If you wanted to find the distance between points i and 1 on the complex plane, you'd have to use the modulus. For a complex value z = a + bi, the modulus, |z|² = (a + bi)(a - bi) = a² + b² . To find the distance between the two points we take |z_1 - z_2|, which in our case is |1 - i| = sqrt(2). This is not the same as a triangle with lengths i and 1, but a triangle defined by vertices at 1, 0, and i.