The area bounded by `|z|geq4`,` (1-i)z+(1+i)barzleq32sqrt(2)`, positive real axis and positive imaginary axis is equal to

" The area of the region bounded by the curve "y=1-x^(2)" ,positive "x" -axis and positive "y" axis is "

If |z^(2)-1|=|z|^(2)+1, then show that z lies on the imaginary axis.

If a is a positive integer,z=a+2i and z|z|-az+1=0 then

Let z_(1) and z_(2) be complex numbers such that z_(1)!=z_(2) and |z_(1)|=|z_(2)| If z_(1) has positive real part and z_(2) has negative imaginary part then (z_(1)+z_(2))/(z_(1)-z_(2)) may be (A) zero (B) real and positive (C) real and negative (D) purely imaginary

If z_(1) and z_(2) are complex numbers such that z_(1) ne z_(2) and |z_(1)|= |z_(2)| . If z_(1) has positive real part and z_(2) has negative imaginary part, then ((z_(1) +z_(2)))/((z_(1)-z_(2))) may be

Let z_(1) and z_(2) be complex numbers such that z_(1)!=z_(2) and |z_(1)|=|z_(2)|. If z_(1) has positive real part and z_(2) has negative imaginary part,then (z_(1)+z_(2))/(z_(1)-z_(2)) may be zero (b) real and positive real and negative (d) purely imaginary

If |z^2-1|=|z|^2+1 , then show that z lies on the imaginary axis.

Area bounded by (y-2)^2=x-1, x-2y+4=0 and positive coordinate axis, is