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

If x +iy = (a + ib) / (a - ib) , prove that x^2 + y^2 = 1 .

If x + iy = (a + ib)/(a - ib), prove that x ^(2) + y ^(2) =1.

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

If (a + 3i) / (2 + ib) = 1 - i, show that 5a - 7b = 0.

Solve the following: If a = (-1 + sqrt(3)i) / 2 , b = (-1 - sqrt(3)i) / 2 , show that a^2 = b and b ^2 = a

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

Find a and b if: (a + ib) + (1 + i) = 2 + i

Fina a and b if (a + ib) (1 + i) = 2 + i

Express the following in the form of a + ib, where a, b in R , i = sqrt-1 . State the value of a and b. (3 + 2i) / (2 - 5i) + (3 - 2i) / (2 + 5i)