Let the complex number `alpha` and `1/alpha` lies `abs(z-z_o)^2=4` and `abs(z-z_o)^2=16` respectively, where `z_0=1+i` . Then, the value of `100|alpha|^2` is

Let the complex numbers alpha and (1)/(bar(alpha)) lie on the circles |z-z_(0)|^(2)=4 and |z-z_(0)|^(2)=16 respectively,where, [z_(0)=1+i .Then,the value of 100| alpha|^(2) is

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

For complex number z,|z-1|+|z+1|=2 then z lies on

Let z be those complex numbers which satisfy |z+5| =-10 i= sqrt(-1) If the maximum value of |z+1|^(2) is alpha+beta sqrt(2) , then the value of (alpha+beta) is

For a complex number Z, if one root of the equation Z^(2)-aZ+a=0 is (1+i) and its other root is alpha , then the value of (a)/(alpha^(4)) is equal to

For a complex z , let Re(z) denote the real part of z . Let S be the set of all complex numbers z satisfying z^(4)- |z|^(4) = 4 iz^(2) , where I = sqrt(-1) . Then the minimum possible value of |z_(1)-z_(2)|^(2) where z_(1),z_(2) in S with Re (z_(1)) gt 0 and Re (z_(2)) lt 0 , is ....

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

Consider the locus of the complex number z in the Argand plane given by Re(z)-2=|z-7+2i|. Let P(z_(1)) and Q(z_(2)) be two complex numbers satisfying the given locus and also satisfying arg ((z_(1)-(2+alpha i))/(z_(2)-(2+alpha i)))=(pi)/(2)(alpha in R). Find the minimum value of PQ .[Note: Re(z) denotes real part of complex number z and i^(2)=-1 ]