Let `z=1-t+isqrt(t^2+t+2)`, where `t` is a real parameter.the locus of the z in argand plane is

Let z=t^2-1+sqrt(t^4-t^2),w h e r et in R is a parameter. Find the locus of z depending upon t , and draw the lous of z in the Argand plane.

If the imaginary part of (2z + 1)/(iz + 1) is -2 , then show that the locus of the point representing z in the argand plane is straight line.

The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 t= 0 & sqrt3 tx +ty-4 sqrt3=0 (where t is a parameter) is a hyperbola whose eccentricity is:

Find the path traced by the point ( at^(2) ,2at) where t is the parameter and a is a constant.

A curve in the xy-plane is parametrically given by x=t+t^3a n dy=t^2,w h e r et in R is the parameter. For what value(s) of t is (dy)/(dx)=1/2? 1/3 b. 2 c. 3 d. 1

If f(x)=(t+3x-x^2)/(x-4), where t is a parameter that has minimum and maximum, then the range of values of t is (0,4) (b) (0,oo) (-oo,4) (d) (4,oo)

If z is a complex number such taht z^2=( barz)^2, then find the location of z on the Argand plane.

Prove that the locus of the centroid of the triangle whose vertices are (acost ,asint),(bsint ,-bcost), and (1,0) , where t is a parameter, is circle.

Prove that |Z-Z_1|^2+|Z-Z_2|^2=a will represent a real circle [with center (|Z_1+Z_2|^//2+) ] on the Argand plane if 2ageq|Z_1-Z_1|^2

The area bounded by the curves arg z = pi/3 and arg z = 2 pi /3 and arg(z-2-2isqrt3) = pi in the argand plane is (in sq. units)