[" Let "a,b,x" and "y" be real numbers such that "a-b=1" and "],[y!=0" .If the complex number "z=x+" iy satisfies "],[Im((az+b)/(z+1))=y" ,then which of the following is(are) "],[" possible value(s) of "x" ? "]

Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the complex number z=x+i y satisfies I m((a z+b)/(z+1))=y , then which of the following is (are) possible value9s) of x?| -1-sqrt(1-y^2) (b) 1+sqrt(1+y^2) -1+sqrt(1-y^2) (d) -1-sqrt(1+y^2)

Let a , b ,xa n dy be real numbers such that a-b=1a n dy!=0. If the complex number z=x+i y satisfies I m((a z+b)/(z+1))=y , then which of the following is (are) possible value9s) of x? (a)-1-sqrt(1-y^2) (b) 1+sqrt(1+y^2) (c)-1+sqrt(1-y^2) (d) -1-sqrt(1+y^2)

Z is a complex number.If a=|x|+|y| and b=sqrt(2)|x+iy| then which of the following is true- -

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

For any complex number w=c+id let arg(w) in (-pi,pi] , where i =sqrt(-1) . Let alpha and beta be real number such that all complex number z=x+iy satisfying arg((z+alpha)/(z+beta))=pi/4 , the ordered pair (x,y) lies on the circle (x^2+y^2+5x-3y+4=0) Then which of the following statement is(are) TRUE?

Let a, x, b in A.P, a, y, b in GP a, z, b in HP where a and b are disnict positive real numbers. If x = y + 2 and a = 5z , then which of the following is/are COR RECT ?

Let a, x, b in A.P, a, y, b in GP a, z, b in HP where a and b are disnict positive real numbers. If x = y + 2 and a = 5z , then which of the following is/are COR RECT ?

If z=x+iy satisfies amp(z-1)=amp(z+3) then the value of (x-1):y is equal to

Let x, y, z be positive real numbers such that x + y + z = 12 and x^3y^4z^5 = (0.1)(600)^3 . Then x^3+y^3+z^3 is