Let `z_(1),z_(2) " and " z_(3)` be three complex numbers in AP.
`bb"Statement-1"` Points representing `z_(1),z_(2) " and " z_(3)` are collinear `bb"Statement-2"` Three numbers a,b and c are in AP, if b-a=c-b

Let z_(1)z_(2)andz_(3) be three complex numbers and a,b,cin R, such that a+b+c=0andaz_(1)+bz_(2)+cz_(3)=0 then show that z_(1)z_(2)and z_(3) are collinear.

If the points represented by complex numbers z_(1)=a+ib, z_(2)=c+id " and " z_(1)-z_(2) are collinear, where i=sqrt(-1) , then

If z_(1), z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, then find arg ((z_(1))/(z_(4)))+arg((z_(2))/(z_(3))) .

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 arg (z_(1))-arg(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear.

z_(1) and z_(2) are two complex number such that |z_(1)|=|z_(2)| and arg (z_(1))+arg(z_(2))=pi , then show that z_(1)=-barz_(2)

Consider the curves on the Argand plane as " "{:(C_(1):arg(z)=pi/4","),(C_(2):arg(z)=(3pi)/(4)):} and C_(3):arg(z-5-5i)=pi," where " i=sqrt(-1). bb"Statement-1" Area of the region bounded by the curves C_(1),C_(2) " and " C_(3) " is " 25/2 bb"Statement-2" The boundaries of C_(1),C_(2) " and " C_(3) constitute a right isosceles triangle.

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

If z is a complex number in the argand plane, the equation |z-2|+|z+2|=8 represents

For complex number z =3 -2i,z + bar z = 2i Im(z) .

If x, 2y and 3z are in AP where the distinct numbers x,y and z are in GP, then the common ratio of the GP is