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 (x+iy)^(1//3)=a+ib ,show that x/a+y/b=4(a^2-b^2)

If (a+ib)(c+id)=x+iy ,prove that x^2+y^2=(a^2+b^2)(c^2+d^2)

If a+ ib= 0, prove that a= b= 0 where a, b in R .

If G.M. of a and b is (a^(n+1)+b^(n+1))/(a^n+b^n) ,then prove that n=-1/2 .

If A+B=pi/4 ,prove that (1+tan A)(1+tan B)=2

If log((a+2b)/4)=1/2(loga+logb) ,then prove that a^2+4b^2=12ab

If the circles x ^2 + y ^2 + 2ax + c = 0 and x ^2 + y ^2 +2by + c = 0 touch each other, prove that 1/a ^2 + 1 b ^2 = 1/c

If a, b, c are in A.P. and a, b, c + 1 are in G.P. then prove that 4a=(a-c)^2 .

If a,b,c are positive unequal real numbers then prove that a^2+b^2+c^2=1=x^2+y^2+z^2 ,then prove that az+bx+cyle1 .