For all complex numbers `z_1,z_2` satisfying `|z_1|=12` and `|z_2-3-4i|=5`, find the minimum value of `|z_1-z_2|`

Let Z_(1) and Z_(2) be two complex numbers satisfying |Z_(1)|=9 and |Z_(2)-3-4i|=4 . Then the minimum value of |Z_(1)-Z_(2)| is

Let z be a complex number satisfying |z+16|=4|z+1| . Then

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

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

It is given that complex numbers z_1a n dz_2s a t i sfy|z_1|=22a n d|z_2|=3. If the included angled of their corresponding vectors is 60^0 , then find the value of |(z_1+z_2)/(z_1-z_2)| .

Complex numbers z_(1) and z_(2) satisfy |z_(1)|=2 and |z_(2)|=3 . If the included angle of their corresponding vectors is 60^(@) , then the value of 19|(z_(1)-z_(2))/(z_(1)+z_(2))|^(2) is

If z_(1),z_(2)andz_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|z_(1)+z_(2)+z_(3)|=1 , find the value of |1/z_(1)+1/z_(2)+1/z_(3)| .

If z_1, z_2 are two complex numbers (z_1!=z_2) satisfying |z1^2-z2^2|=| z 1^2+ z 2 ^2-2( z )_1( z )_2| , then a. (z_1)/(z_2) is purely imaginary b. (z_1)/(z_2) is purely real c. |a r g z_1-a rgz_2|=pi d. |a r g z_1-a rgz_2|=pi/2

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