If a+ib=`frac{1+i}{1-i}`, then prove that (`a^2`+`b^2`)=1

Similar Questions

Explore conceptually related problems

If x -iy = frac{a-ib}{c-id} , then prove that ( x^2 + y^2 ) = frac{a^2+b^2}{c^2+d^2}

If (frac{1+i}{1-i})^x = 1, then

(frac{1+i}{1-i})^2 =?

If (a+ib) = frac{(x+i)^2}{2x^2+1} , prove that a^2 + b^2 = frac{(x^2+1)^2}{(2x^2+1)^2}

If x+iy= frac{a+ib}{a-ib} , prove that x^2 + y^2 = 1

If a= frac{-1+sqrt3 i}{2} , b= frac{-1-sqrt3 i}{2} , then show that a^2 =b and b^2 =a

If a + ib = (1 + i) / (1 - i) , prove that a^2 + b^2 = 1

If x-iy = sqrt (frac{a-ib}{c-id}) , prove that (x^2+y^2) = frac{a^2+b^2}{c^2+d^2}

If frac{a+3i}{2+ib} = 1-i, show that (5a-7b)=0

If [frac{1-i}{1+i}]^96= a+ib , then (a,b) is