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)

(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 , prove that p^2+q^2 = (a^2+1)^2/(4a^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 , prove 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))

I. p^(2)= 4 II. q^(2) + 4q =- 4

if q is the mean proportional between p and r , prove that : p^(2) - q^(2) + r^(2) = q^(4) ((1)/(p^(2))-(1)/(q^(2)) + (1)/(r^(2))) .

If (a+i)^2/(2a-1)=p+iq then find the values of (p^2+q^2)

If (cosA)/(cosB)=p,(sinA)/(sinB)=q ,then show that (p^(2)(1-q^(2)))/(p^(2)-q^(2))=cos^(2)A .