Let `z` be a complex number having the argument theta,`0 < theta < pi/2`, and satisfying the equation `|z-3i|=3.` Then find the value of `cot theta-6/z`

Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a cannot take the value

Let z_1=10+6i and z_2=4+6idot If z is any complex number such that the argument of ((z-z_1))/((z-z_2)) is pi/4, then prove that |z-7-9i|=3sqrt(2) .

Let z be a complex number satisfying the equation (z^3+3)^2=-16 , then find the value of |z|dot

Let z=x+i y be a complex number, where xa n dy are real numbers. Let Aa n dB be the sets defined by A={z :|z|lt=2}a n dB={z :(1-i)z+(1+i)bar z geq4} . Find the area of region AnnB

The argument of the complex number z=r(sin theta+ icos theta), r gt 0 is

Let z ne 1 be a complex number and let omeg= x+iy, y ne 0 . If (omega- bar(omega)z)/(1-z) is purely real, then |z| is equal to

Let z_(1)" and "z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number further, assume that the origin, z_(1)" and "z_(2) form an equilateral triangle, then

Let z be any non zero complex number then arg z + arg barz =

Let z be a complex number satisfying |z+16|=4|z+1| . Then

If the argument of (z-a)(barz-b) is equal to that ((sqrt(3)+i)(1+sqrt(3)i)/(1+i)) where a,b,c are two real number and z is the complex conjugate o the complex number z find the locus of z in the rgand diagram. Find the value of a and b so that locus becomes a circle having its centre at 1/2(3+i)