Let a,b,x and y be real numbers such that a-b =1 and `y ne 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)

If x, y, z are positive real numbers such that x+y+z=a, then

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

For every real number age 0 , find all the complex numbers z that satisfy the equation 2|z|-4az+1+ ia =0

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 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

A variable complex number z=x+iy is such that arg (z-1)/(z+1)= pi/2 . Show that x^2+y^2-1=0 .

If logy^(x)=(alog_(z)y)=(blog_(x)z=ab, then which of the following pairs of values for (a,b) is not possible ?

If the complex number z=x+i y satisfies the condition |z+1|=1, then z lies on (a)x axis (b) circle with centre (-1,0) and radius 1 (c)y-axis (d) none of these

If the complex numbers x and y satisfy x^3-y^3=98i and x-y=7i ,then x y=a+i b ,where a ,b , in Rdot The value of (a+b)//3 equals ______.