Let the complex number z be root of the equation 11z10+10iz9+10iz-11=0, then which of the following statement(s) is/are correct?

11z10+10iz9+10iz-11=0  ⇒z911z +10i=11-10iz  ⇒z9=11-10iz11z+10i⇒z9=11i+10z11z+10i ⇒11i+10z2-11z+10i2=112-1021-z2 =211-z2  for z<1⇒11i+10z2-11z+10i2>0   ⇒ z9==11i+10z11z+10i>1⇒z9>1 which contradicts with z<1for  z>1 we get z9<1   therefore z=1