harder complex number question (1 Viewer)

[conics2008]

The complex number w1 and w2 have mod 1 and arg alpha 1 and alpha 2 respectivley

where 0<alpha1<alpha2<pi/2


i) draw the diagram ( done)
ii) show that arg(w1-w2)= 1/2(alpha1+alpha2-pi) ( dont know how )

Thanks

PS: Im sorry for drowing this fourm with maths questions, but its just the questions im having trouble with .

 

[sicmacao]

The complex number w1 and w2 have mod 1 and arg alpha 1 and alpha 2 respectivley


where 0<ALPHA1<ALPHA2


i) draw the diagram ( done)
ii) show that arg(w1-w2)= 1/2(alpha1+alpha2-pi) ( dont know how )

Thanks

PS: Im sorry for drowing this fourm with maths questions, but its just the questions im having trouble with .

If you draw the figure, the complex number w1-w2 represent the base of the isosceles triangle. The apex of the isosceles triangle has angle alpha1-alpha2. Hence the base angle is 1/2(pi - (alpha1-alpha2)). By exterior angle of the triangle the arg(w1-w2) = 1/2(pi - (alpha1-alpha2)) + alpha1 = 1/2(alpha1+alpha2+pi).