Complex Numbers Vector Help (1 Viewer)

[AreYouAlright?]

I'm so lost when it comes to questions involving complex numbers and vectors, can someone please explain to me how you get to the statement that Q is z-u in this solution attatched.

 

[Trev]

I think they meant Q is the complex number (u-v).

 

[AreYouAlright?]

But how do you get that statement, how do we know that Q is the complex no (u-v)?

 

[Trev]

If you subtract the ordinates of v from u you get the position of Q because in the diagram length BA is equal to length OQ, and they are parallel...

 

[Stefano]

But how do you get that statement, how do we know that Q is the complex no (u-v)?

With complex vectors it doesn't matter where the 'lines' are. In this case, BA=OQ because they have the same length and are parralel.

So, working with BA:

To get from B to A we must;
1. Go from B to O (-OB)
2. Go from O to A (OA)

Adding these;
OA-OB = u-v

And since OQ = BA;
OQ = u-v


All good?

 

[.ben]

how do you rotate vectors through non 90 degree angles?

 

[Trev]

If you want to lengthen the vector by 3, and rotate the vector 135 degrees (3pi/2) clockwise you would mutliply the vector by 3cis(-3pi/4) for example.
Hope that sorta helps

 

[robbo_145]

multiply by Cisθ where θ is the angle in radians

hence rotation by Π/2 anti clockwise is the multiplication by i
as Cis(Π/2) = i

edit: Trev was too quick

 

[AreYouAlright?]

With complex vectors it doesn't matter where the 'lines' are. In this case, BA=OQ because they have the same length and are parralel.

So, working with BA:

To get from B to A we must;
1. Go from B to O (-OB)
2. Go from O to A (OA)

Adding these;
OA-OB = u-v

And since OQ = BA;
OQ = u-v


All good?

Thanks heaps that was exactly how i needed to hear it explained... lol it's hard i can only think about maths problems in a certain linear way.

 

[Stefano]

Thanks heaps that was exactly how i needed to hear it explained... lol it's hard i can only think about maths problems in a certain linear way.

No problem mate! I'm glad i've managed to help someone. Ussually I'm the one asking for help! haha.

 

[.ben]

o cool thanks trev and robbo!