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

Find the point of intersection of the curves a r g(z-3i)=(3pi)/4 and arg(2z+1-2i)=pi//4.

Given that the two curves a r g(z)=pi/6 and |z-2sqrt(3)i|=r intersect in two distinct points, then a. [r]!=2 b. 0 < r < 3 c. r=6 d. 3 < r < 2sqrt(3) (Note : [r] represents integral part of r)

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 | d. none of these

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

Find the center of the are 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.

Let z_1a n dz_2 be two distinct complex numbers and let z=(1-t)z_1+t z_2 for some real number t with 0 |z-z_1|+|z-z_2|=|z_1-z_2| (z-z_1)=(z-z_2) |z-z_1 z -( z )_1z_2-z_1( z )_2-( z )_1|=0 a r g(z-z_1)=a r g(z_2-z_1)

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 whose radius is 5sqrt(2) whose radius is 5 whose length (of arc) is (15pi)/(sqrt(2)) whose centre is -2-5i

Given that the complex numbers which satisfy the equation | z bar z ^3|+| bar z z^3|=350 form a rectangle in the Argand plane with the length of its diagonal having an integral number of units, then area of rectangle is 48 sq. units if z_1, z_2, z_3, z_4 are vertices of rectangle, then z_1+z_2+z_3+z_4=0 rectangle is symmetrical about the real axis a r g(z_1-z_3)=pi/4or(3pi)/4