If `a r g(z)<0,` then `a r g(-z)-"a r g"(z)` equals `pi` (b) `-pi` (d) `-pi/2` (d) `pi/2`

Write the value of a r g(z)+a r g(barz ) .

Given that the two curves a r g(z)=pi/6a n d|z-2sqrt(3)i|=r intersect in two distinct points, then

If z is a complex number such that -pi//2lt=a r g zlt=pi//2, then which of the following inequality is true? (a) |z- z |lt=|z|(a r g z-a r g z ) b. |z- z |geq|z|(a r g z-a r g z ) c. |z- z |<(a r g z-a r g z ) d. none of these

If z_1a n dz_2 are conjugate to each other then find a r g(-z_1z_2)dot

For |z-1|=1, show that tan{[a r g(z-1)]/2}-((2i)/z)=-i

Find the center of the arc represented by a r g[(z-3i)//(z-2i+4)]=pi//4 .

Plot the region represented by pi/3lt=a r g((z+1)/(z-1))lt=(2pi)/3 in the Argand plane.

The maximum value of |a r g(1/(1-z))| for |z|=1, z!=1 is given by.

Locus of complex number satisfying "a r g"[(z-5+4i)/(z+3-2i)]= -pi/4 is the arc of a circle (a)whose radius is 5sqrt(2) (b)whose radius is 5 (c)whose length (of arc) is (15pi)/(sqrt(2)) (d)whose centre is -2-5i

If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z, is