If `2+z+z^4=0, where z` is a complex number then (A) `1/2 lt|z|lt1` (B) `1/2lt|z|lt1/3` (C) `|z|ge1` (D) none of these

If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+(z^2+1/z^2)^2+....+(z^6+1/z^6)^2 is

If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2 (c) 1/4 (d) None of these

If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2 (c) 1/4 (d) None of these

Find the Area bounded by complex numbers arg|z|lepi/4 and |z-1|lt|z-3|

z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0 , then |z| is equal to

If z_1 and z_2 are complex numbers such that |z_1-z_2|=|z_1+z_2| and A and B re the points representing z_1 and z_2 then the orthocentre of /_\OAB, where O is the origin is (A) (z_1+z_2)/2 (B) 0 (C) (z_1-z_2)/2 (D) none of these

If z_1 is a root of the equation a_0z^n+a_1z^(n-1)+........+ (a_(n-1)) z + a_n=3, where |a_i| lt 2 for i=0,1,.....n, then (a). |z|=3/2 (b). |z| lt 1/4 (c). |z| gt 1/4 (d). |z| > 1/3

If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(z)=pi/4 b. arg(z)=pi/2 c. |z|=1/2 d. |z|=2

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

If z is any complex number such that |z+4|lt=3, then find the greatest value of |z+1|dot