Is traveling east in a positive imaginary direction the same thing as traveling north in a positive real direction? So, if someone says, "go $-5$ miles east" you know that that means, "go $5$ miles west". If someone says, "go $5i$ miles east", does that mean "go $5$ miles north"?
 A: That's a strange but interesting question. I think that with the right conventions a reasonable answer is "yes".
Start by thinking about the complex numbers in the usual way as the Euclidean coordinate plane. Then it's reasonable to think of the four compass directions ENWS as specifying travel parallel to the coordinate axes in the obvious way. "Adding $5$" to any complex number takes you five units to the right (east). "Adding $5i$" to any complex number takes you five units up (north).
Then of course "go $5$ miles northeast" is the same as "go $5/\sqrt{2}$ miles east,
 then $5/\sqrt{ 2}$ miles north", or just "go $5(1+i)/\sqrt{2}$".
All in all, somewhat weird but a nice idea.
A: Sometimes the complex numbers are associated with the complex plane in which the Cartesian coordinates $(a, b)$ are identified with $a + bi$. Associating the plane with the standard orientation of a North-South-East-West map, I can see why traveling east or west could be associated with real numbers (just as real numbers are often depicted on the number line, i.e., a horizontal line) but it seems to me that, from this perspective, the imaginary numbers would be better referred to as being north or south.
That said: This terminology seems to me quite nonstandard, so I would not expect any of North, South, East, or West to be readily interpreted in the context of "complex" directions.
