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

Given that the two curves a r g(z)=pi/6a n d|z-2sqrt(3)i|=r intersect in two distinct points, then [r]!=2 b. 0

If z_1, z_2, z_3 are three complex, numbers and A=[[a r g z_1,a r g z_3,a r g z_3],[a r g z_2,a r g z_2,a r g z_1],[a r g z_3,a r g z_1,a r g z_2]] Then A divisible by a r g(z_1+z_2+z_3) b. a r g(z_1, z_2, z_3) c. all numbers d. cannot say

If z_1,z_2,z_3,z_4 be the vertices of a parallelogram taken in anticlockwise direction and |z_1-z_2|=|z_1-z_4|, then sum_(r=1)^4(-1)^r z_r=0 (b) z_1+z_2-z_3-z_4=0 a r g(z_4-z_2)/(z_3-z_1)=pi/2 (d) None of these

Given that the complex numbers which satisfy the equation | z z ^3|+| 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

If z_1=10+6i and z_2=4+2i be two complex numbers and z be a complex number such that a r g((z-z_1)/(z-z_2))=pi/4 , then locus of z is an arc of a circle whose (a) centre is 5+7i (b) centre is 7+5i (c) radius is sqrt(26) (d) radius is sqrt(13)

If r=abs(z),theta="arg"(z)"and"z=2-2itan((5pi)/8) then find (r, theta)

Let z_1a n dz_2 be two complex numbers such that ( z )_1+i( z )_2=0a n d arg(z_1z_2)=pidot Then, find a r g(z_1)dot

Identify the locus of z if bar(z)=bar(a)+(r^(2))/(z-a)

Consider f" ":" "N ->N , g" ":" "N ->N and h" ":" "N ->R defined asf" "(x)" "=" "2x , g" "(y)" "=" "3y" "+" "4 and h" "(z)" "=" "s in" "z , AA x, y and z in N. Show that ho(gof ) = (hog) of.