SOLUTION: If z1 and z2 are complex numbers and |z2| = 4 , |z1|+ i×|z2|= 3 + 4i , then value of |z2 + i × z1|=... [ 9, 16, 5 , 25 ]

Read the problem attentively.  It says that  |z1|+ i×|z2| = 3 + 4i.


This means that  |z1| = 3,  |z2| = 4.


Now, due to the "triangle" inequality for adding complex number, 
the general rule is that for all complex numbers z1 and z2

    |z2 + z1| <= |z2| + |z1|.


Hence, in your case,  |z2 + i*z1|  can not be greater than 4 + 3 = 7.


Thus, options  9, 16, 25 do not work.


The only acceptable option is the remaining value of 5.