Pretty sure its a troll?
Suppose j=a+ib for b nonzero and real, since j is not real.
J^2= a^2-b^2+2abi =1.
Collecting real and imaginary parts, a^2-b^2=1 and ab=0. Since b non zero, a must be 0. Thus -b^2 =1 so b^2=-1 which is not possible since b was assumed to be real. Thus no real b can...