`" The locus of the point representing the complex number "z" for which "|z+10i|^(2)-|z-10i|^(2)=20," is (where "i=sqrt(-1))`

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

The locus of the points representing the complex numbers z for which |z|-2=|z-i|-|z+5i|=0 , is

Find the complex number z for which |z| = z + 1 + 2i.

The points representing complex number z for which |z+2+ 3i| = 5 lie on the locus given by

If |z-1-i|=1 , then the locus of a point represented by the complex number 5(z-i)-6 is

Show that the area of the triagle on the argand plane formed by the complex numbers Z, iz and z+iz is (1)/(2)|z|^(2)," where "i=sqrt(-1).

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