If `x` is real and `(1-ix)/(1+ix)=m + i n,` show that `m^2 + n^2=1.`

If a,b, xin R and if (1-ix)/(1+ix)=a-ib ,prove that a^2 + b^2 = 1 .

If a,b, x in R and (1-ix)/(1+ix)=a+ib ,then prove that a^2+b^2=1

If 1/ (m+i n) - (x-iy)/(x+iy) =0, where x,y,m,n are real and x+iy!=0 and m+i n!=0 , prove that m^2+n^2=1 .

If 1/ (m+i n) - (x-iy)/(x+iy) =0, where x,y,m,n are real and x+iy!=0 and m+i n!=0 , prove that m^2+n^2=1 .

if (1-ix)/(1+ix)=a-ib ,then prove that a^2+b^2=1 (a,b x are real).

If a,b are real and a^(2)+b^(2)=1, then show that, the equation (1-ix)/(1+ix)=a-ib is satisfied by a real value of x.

Show that a real value of 'x' will satisfy the equation (1- ix )/(1+i x)=a-i b , where a^(2)+b^(2)=1 , a, b are real.

Show that a real value of x\ will satisfy the equation (1-ix)/(1+ix)=a-i b\ if\ a^2+b^2=1 , when a\ , b are real.

Show that a real value of x will satisfy the equation (1-ix)/(1+ix)= a -ib if a^2+b^2=1 , where a, b are real.

If 2 cos alpha = x + (1)/(x) and 2 cos beta = y + (1)/(y) , show that x^(m) y^(n) + (1)/(x^(m)y^(n)) = 2 cos (m alpha + n beta)