If `t` and `c` are two complex numbers such that `|t|!=|c|,|t|=1a n dz=(a t+b)/(t-c), z=x+i ydot` Locus of `z` is (where a, b are complex numbers) a. line segment b. straight line c. circle d. none of these

If |z+barz|+|z-barz|=2 then z lies on (a) a straight line (b) a set of four lines (c) a circle (d) None of these

If z_1a n dz_2 are two nonzero complex numbers such that = |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to -pi b. pi/2 c. 0 d. pi/2 e. pi

a ,b ,c are three complex numbers on the unit circle |z|=1, such that a b c=a+b+c dot Then find the value of |a b+b c+c a|dot

If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqrt(2)+1 c. sqrt(2)-1 d. none of these

If a ,b ,c and u ,v ,w are the complex numbers representing the vertices of two triangles such that (c=(1-r)a+r b and w=(1-r)u+r v , where r is a complex number, then the two triangles (a)have the same area (b) are similar (c)are congruent (d) None of these

If z is complex number, then the locus of z satisfying the condition |2z-1|=|z-1| is (a)perpendicular bisector of line segment joining 1/2 and 1 (b)circle (c)parabola (d)none of the above curves

The number of complex numbers z satisfying |z-3-i|=|z-9-i|a n d|z-3+3i|=3 are a. one b. two c. four d. none of these

If z_1a n dz_2 are two complex numbers and c >0 , then prove that |z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot

If |z|=1, then the point representing the complex number -1+3z will lie on a. a circle b. a parabola c. a straight line d. a hyperbola

If z=(i)^((i)^(i)) w h e r e i=sqrt(-1),t h e n|z| is equal to a. 1 b. e^(-pi//2) c. e^(-pi) d. none of these