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

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|

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

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

If Pa n dQ are represented by the complex numbers z_1a n dz_2 such that |1/z_2+1/z_1|=|1/(z_2)-1/z_1| , then O P Q(w h e r eO) is the origin is equilateral O P Q is right angled. the circumcenter of O P Qi s1/2(z_1+z_2) the circumcenter of O P Qi s1/3(z_1+z_2)

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

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|

Let i=sqrt(-1) Define a sequence of complex number by z_1=0, z_(n+1) = (z_n)^2 + i for n>=1 . In the complex plane, how far from the origin is z_111 ?

It z_(1) and z_(2) are two complex numbers, such that |z_(1)| = |z_(2)| , then is it necessary that z_(1) = z_(2) ?

If z_(1)=2-i, z_(2)=1+i , find |(z_(1)+z_(2)+1)/(z_(1)-z_(2)+1)| .