Python 2, 72 bytes

n=s=1;x=[] exec'x+=[s]*n+[s*1j]*n;n+=1;s=-s;'*input() print sum(x[:n-1]) 

Indexing is 0-based, output is a complex number. Test it on Ideone.

Python 2, 72 62 bytes

n=2;x=[] exec'x+=n/2*[1j**n];n+=1;'*input() print-sum(x[:n-2]) 

Thanks to @xnor for suggesting and implementing the quarter-turn idea, which saved 10 bytes.

Indexing is 0-based, output is a complex number. Test it on Ideone.