What is the difference between いかなきゃ(ikanakya) and いかなきゃいけない(ikanakya ikenai)? From what I read in a forum, ikanakya translates to 'I have to go'. The confusing thing is why does adding ikenai to ikanakya (ikanakya ikenai) mean exactly the same thing (I have to go) and not 'I do not have to go'?
The full, polite form of the expression is ～なければいけません or ～なければなりません which both mean "I must ~", and if you tried to translate it bit-by-bit you'd get something like "Not doing ~ is no good". (Note that while いけません does come from the verb 行く, it doesn't mean "I can't go", it means something more like "It's no good".)
In plain form, いけません becomes いけない, and in casual speech ～なければ gets elided into ～なきゃ (the same way "going to" becomes "gonna"). So the construction for "must" is ～なきゃいけない.
However, the ～なきゃ construct is pretty much only used in this context, meaning that the いけない can be taken for granted, and like many other things in Japanese it's fine to leave off the bit that everyone knows is meant to be there. Hence, ～なきゃ is just an abbreviation for the longer construct.