It is given that complex numbers `z_1` and `z_2` satisfy `|z_1|=2 `and `|z_2|=3.` If the included angled of their corresponding vectors is `60^0` , then find the value of `19|(z_1-z_2)/(z_1+z_2)|^2` .

For all complex niumbers z_1, z_2 satisfying absz_1=12 and abs(z_2-3-4i)=5 , the minimum value of abs(z_1-z_2) is

For all complex numbers z_(1),z_(2) satisfying |z_(1)|=12 and |z_(2) -3-4i|=5, then minimum value of |z_(1)-z_(2)| is-

The complex numbers z_1,z_2 and z_3 satisfying (z_1-z_3)/(z_2-z_3)=(1-isqrt3)/2 are the verticles of a triangle which is:

Find the greatest and the least value of |z_1+z_2| if z_1=24+7i and |z_2|=6.

For any two complex numbers z_1 and z_2 , , prove that Re (z_1 z_2) = Re z_1 Re z_2 – Imz_1 Imz_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

If z be a complex number satisfying z^4+z^3+2z^2+z+1=0 then absz is equal to

If P and Q are represented by the complex numbers z_1 and z_2 such that |1/z_2+1/z_1|=|1/(z_2)-1/z_1| , then a) O P Q(w h e r eO) is the origin of equilateral O P Q is right angled. b) the circumcenter of O P Q is 1/2(z_1+z_2) c) the circumcenter of O P Q is 1/3(z_1+z_2)

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

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