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.

Find the radius and centre of the circle z bar(z) - (2 + 3i)z - (2 - 3i)bar(z) + 9 = 0 where z is a complex number

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

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) .

z_1, z_2, z_3,z_4 are distinct complex numbers representing the vertices of a quadrilateral A B C D taken in order. If z_1-z_4=z_2-z_3a n d"a r g"[(z_4-z_1)//(z_2-z_1)]=pi//2 , the quadrilateral is a. rectangle b. rhombus c. square d. trapezium

The locus of z such that arg[(1-2i)z-2+5i]= (pi)/(4) is a

Represents the variable complex number z . Find the locus of P if arg((z-1)/(z+3))=(pi)/(2) .

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

Given the complex number z = 2 +3i, represent the complex numbers in Argand diagram. z, -iz, and z - iz.