May be you know it or not a two dimensional vector can be represented by a complex number.Why i have written this statement you will just know when you will see its solution
a = 3i + mj and b = 2i - nj are perpendicular to each other ,so their dot product
will be zero.
[tex]i.e a.b = 0\\
(3i + mj) .(2i - nj)=0\\
6-mn=0\\
mn=6[/tex]j
vector b = 2i - nj and vector c = ni + 8j are parallel to each other.[tex]2i - nj = k (ni + 8j)
2/n = -n/8
n^{2} =-16
n=4i[/tex]j
mn = 6
so m=6/4i
m=3/2i
m=3i^{4}/2i
m = 3i^{3}/2
m= -3i/2 as(i^{4} =1, i^{3} = -i[/tex][/tex]
