For any complex number `z` find the minimum value of `|z|+|z-2i|`

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

If z is a complex number, then find the minimum value of |z|+|z-1|+|2z-3|dot

If Z^5 is a non-real complex number, then find the minimum value of | (Imz^5)/(Im^5z) |

Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

The complex number z satisfies z+|z|=2+8i . find the value of |z|-8

If z is a complex number such that z+|z|=8+ 12i , then the value of |z^2| is equal to

Variable complex number z satisfies the equation |z-1+2i|+|z+3-i|=10 . Prove that locus of complex number z is ellipse. Also, find the centre, foci and eccentricity of the ellipse.

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

For any two complex numbers z_1 and z_2 , prove that |z_1+z_2| =|z_1|-|z_2| and |z_1-z_2|>=|z_1|-|z_2|