Question

Relation between slopes of 2 perpendicular lines in terms of a complex number ???

Answer 1

Hey there !!!!!!!

Let us consider m₁ , m₂ are slopes of two lines L₁ and L₂ which are mutually perpendicular.

The product of slopes of these mutually perpendicular lines= -1

⇒⇒⇒⇒⇒  m₁m₂=-1

But we know that "i" is a complex number and its square is -1.

                      i²=-1
        
                      m₁m₂=-1

So,               m₁m₂=i²

Hope this helped you .............

Answer 2

Let two lines are gven , in the slope form y = m1x + C1
y =m2x + C2
where, m1 and m2 are the slopes of given lines and C1 and C2 are y - intercepts .

we also know,
both lines will be perpendicular when ,
slope of 1st line × slope of 2nd line= -1
e.g m1 × m2 = - 1 ---------(1)
but we know,
i² = -1
use this in equation (1)

then,
m1 × m2 = (-1) = i²

hence,
m1 × m2 = i² is relation between slope of two lines in term of complex number.