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

Represent the complex number z=1+isqrt(3) in the polar form.

Find the locus of the points representing the complex number z for which |z+5|^2-|z-5|^2=10.

Given the complex number z = 2 +3i, represent the complex numbers in Argand diagram. z, -iz, and z - iz.

Given the complex number z = 2 +3i, represent the complex numbers in Argand diagram. z, iz, and z + iz

If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight line c. a pair of straight line d. none of these

The locus of point z satisfying R e(1/z)=k ,w h e r ek is a nonzero real number, is a. a straight line b. a circle c. an ellipse d. a hyperbola

If |z|=1 , then prove that points represented by sqrt((1+z)//(1-z)) lie on one of two fixed perpendicular straight lines.

If from a point P representing the complex number z_1 on the curve |z|=2 , two tangents are drawn from P to the curve |z|=1 , meeting at points Q(z_2) and R(z_3) , then :

Fir any complex number z, the minimum value of |z|+|z-1| is

P represents the variable complex number z find the locus of z if : Re((z+1)/(z+i))=1