Let `barz+bbarz=c,b!=0` be a line the complex plane, where `bar b` is the complex conjugaste of b. If a point `z_1` i the reflection of the point `z_2` through the line then show that `c=barz_1b+z_2barb`

Let barbz+b(barz)=c,b!=0 be a line the complex plane, where bar b is the complex conjugate of b. If a point z_1 i the reflection of the point z_2 through the line then show that c=barz_1b+z_2barb

If a point z_(1) is the reflection of a point z_(2) through the line b barz+barbz=c, b in 0 , in the Argand plane, then b barz_(2)+ barb z_(1)=

Find the complex number z if zbarz = 2 and z + barz=2

If (1+i)z=(1-i) barz , then show that z=-i barz dot

If (1+i)z = (1-i)barz, "then show that "z = -ibarz.

If z(bar(z+alpha))+barz(z+alpha)=0 , where alpha is a complex constant, then z is represented by a point on

Let A(2,0) and B(z) are two points on the circle |z|=2 . M(z') is the point on AB . If the point barz' lies on the median of the triangle OAB where O is origin, then arg(z') is

If z is a complex number such taht z^2=( barz)^2, then find the location of z on the Argand plane.

A,B and C are the points respectively the complex numbers z_(1),z_(2) and z_(3) respectivley, on the complex plane and the circumcentre of /_\ABC lies at the origin. If the altitude of the triangle through the vertex. A meets the circumcircle again at P, prove that P represents the complex number (-(z_(2)z_(3))/(z_(1))) .

If the argument of (z-a)(barz-b) is equal to that ((sqrt(3)+i)(1+sqrt(3)i)/(1+i)) where a,b,c are two real number and z is the complex conjugate o the complex number z find the locus of z in the rgand diagram. Find the value of a and b so that locus becomes a circle having its centre at 1/2(3+i)