Purely imaginary number is a complex number which has only imaginary part ( iy)
But if y=0 the complex number iy will become 0 which is real.
Hence the condition for a number to be purely imaginary is x=0 and
here,
comparinf the given equation with ax + by + c= 0
a = -4, b =1 and c= -3
so ab < 0
hence,
so a perfect positive correlation.