Let `z=x+i y` be a complex number, where `xa n dy` are real numbers. Let `Aa n dB` be the sets defined by `A={z :|z|lt=2}a n dB={z :(1-i)z+(1+i)bar z geq4}` . Find the area of region `AnnB`

Let z be a complex number satisfying |z+16|=4|z+1| . Then

Let z=x+i y be a complex number where xa n dy are integers. Then, the area of the rectangle whose vertices are the roots of the equation z (\bar {z })^3+ \bar{z} z^3=350 is 48 (b) 32 (c) 40 (d) 80

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

If z is non zero complex number, such that 2i z^(2) = bar(z), then |z| is

If z = x + iy is a complex number such that |(z-4i)/(z+ 4i)| = 1 show that the locus of z is real axis.

Let z_(1)" and "z_(2) be two complex numbers such that z_(1)z_(2)" and "z_(1)+z_(2) are real then

Let z ne 1 be a complex number and let omeg= x+iy, y ne 0 . If (omega- bar(omega)z)/(1-z) is purely real, then |z| is equal to

Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a cannot take the value

Let z_1, z_2, z_3 be three complex numbers and a ,b ,c be real numbers not all zero, such that a+b+c=0a n da z_1+b z_2+c z_3=0. Show that z_1, z_2,z_3 are collinear.

The complex number z satisfies z+|z|=2+8i . find the value of |z|-8