If `arg(z - 1) = pi/6` and `arg(z + 1) = 2 pi/3` , then prove that `|z| = 1`.

If |z| = 4 and arg(z) = (5pi)/6 , then z = …………..

If |z_1/z_2|=1 and arg (z_1z_2)=0 , then

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) .

If z = x + iy and arg ((z - i)/(z + 2))= (pi)/(4) . Show that x^(2) + y^(2) + 3x - 3y + 2 = 0 .

IF sin^(-1) X+ sin^(-1) y+ sin^(-1) z= pi , then prove that x^4 +y^4+ z^4 +4x^2 y^2 z^2 = 2(x^2 y^2 +y^2 z^2+z^2x^2).

The area bounded by the curves arg z = pi/3 and arg z = 2 pi /3 and arg(z-2-2isqrt3) = pi in the argand plane is (in sq. units)

arg z= pi if and only if z is a

If z = x + iy and arg ((z-1)/(z+1))=pi/2 , show that x^(2)+y^(2)-1=0 .

A(z_1),B(z_2),C(z_3) are the vertices of the triangle A B C (in clockwise). If /_A B C=pi//4 and A B=sqrt(2)(B C) , then prove that z_2=z_3+i(z_1-z_3)dot