Express the complex number (1+i)/(1-i) in the form x+iy

First of all calculate the complex conjugate of the denominator. The complex conjugate of (1-i) is 1+i.Now multiply the given complex number by (1+i)/(1+i), note that we are not modifying the starting number since we are just multiplying by 1. The product is (1+i)^2/(1-(i)^2), that is (1+i)^2/2. Finally just calculate (1+i)^2=1+2i+(i^2)=2i, thus (1+i)/(1-i)=2i/2=i=0+1*i.