What is the image of Complex?

When I think of complex, something which just goes over my head, its some multidimensional space that fits perfectly in theories satisfies formulae and equations and blocks my head with all its complexity and take some to far away world. Some faculty mentions six dimensional space and Orthogonality of vectors therein with emphasis on what happens when Vector rotates; all I can visualize is a lone little vector  trying to rotate around a point. BY six dimension I see the three sides of room getting round and round to somehow give six perpendicular directions .. Oh God !! then lecturer says periodic trajectories are easy but Orthogonal is complicated  but yes in the neighborhood u can always study the properties easily. Its then when my mind wanders on the view of all natural objects I forget of vectors, equilibrium and rotation of non linear dynamical or linear - all seems so senseless . Why the heck - few theorems which are supposedly the greatest truths in mathematical formulations helping to decipher the real world..but to me it is just a round round rotating word and its all over making no sense..I give up with something which can never be understood -- its just something to struggle with till the last exam . Why don't you get a PC and show the vectors you want me to visualize , why just talk show its properties graphically -- its such a waste .. Non linear Space -- hope somebody understands you well to explain in the best way..