Number of ordered pairs (a,b) of real numbers such that(a+ib)2012=a−ib holds good is

Let z=a+ib⇒z−=a−ib ∴z2012=z− |z|2012=|z−|=|z| |z|(|z|2011−1)=0 ⇒|z|=0 or |z|=1 If |z|=0 ⇒z=0⇒(0,0) If |z|=1,z2012=z− ⇒z2013=zz−=|z|2=1 ⇒2013  values of z