[" (i) If "((a+i)^(2))/((2a-i))=p+" iq.Prove that "],[" pt "4+q^(2)=((a^(2)+1)^(2))/(4a^(2)+1)]

(i) If x+iy=(a+ib)/(a-ib) , prove that x^(2)+y^(2)=1 . (ii) If ((a+i)^(2))/(2a-i)=p+iq , prove that: p^(2)+q^(2)=((a^(2)+1)^(2))/(4a^(2)+1) .

If ((a + i)^(2))/(2a-i) = p + iq, show that p^(2) + q^(2) = (a^(2) + 1)^(2)/(4a^(2) + 1)

If ((a+i)^(2))/(2a-i)= p +qi , show that p^(2) + q^(2)= ((a^(2) + 1)^(2))/(4a^(2) + 1)

If ((a+i)^(2))/((2a-i))=p+iq, show that: p^(2)+q^(2)=((a^(2)+1)^(2))/((4a^(2)+1))

If (a+i)^2/((2a-i))= p + iq , prove that : p^2+q^2 =(a^2+1)^2 /(4a^2+1) .

if a+ib=((u+i)^(2))/(2u-i) then prove that a^(2)+b^(2)=((u^(2)+1)^(2))/(4u^(2)+1)

If ((a+i)^2)/((2a-i))=p+i q , show that: p^2+q^2=((a^2+1)^2)/((4a^2+1)) .

If (a+i)^2/(2a-i)=p+iq then prove that p^2+q^2=((a^2+1)^2/(4a^2+1))

If (a+i)^2/(2a-i) = p+iq , prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

If (x+iy)(p+iq)=(x^(2)+y^(2))i, prove that x=q,y=p