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

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

The region represented by the inequality |2z-3i|<|3z-2i| is

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

Find the modulus of the complex number z=4-i

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

Find the modulus of the complex number z=4+3i

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

P(z_1),Q(z_2),R(z_3)a n dS(z_4) are four complex numbers representing the vertices of a rhombus taken in order on the complex lane, then which one of the following is/ are correct? (z_1-z_4)/(z_2-z_3) is purely real a m p(z_1-z_4)/(z_2-z_3)=a m p(z_2-z_4)/(z_3-z_4) (z_1-z_3)/(z_2-z_4) is purely imaginary It is not necessary that |z_1-z_3|!=|z_2-z_4|

The locus of any point P(z) on argand plane is arg((z-5i)/(z+5i))=(pi)/(4) . Then the length of the arc described by the locus of P(z) is

let z_1=10+6i and z_2=4+6i if z is nay complex number such that argument of (z-z_1)/(z-z_2) is pi/4 the prove that abs(z-7-9i)=3sqrt2