Complex number help (1 Viewer)

[helpfulperson?]

 

[Luukas.2]

Express PQ and PR as vectors in terms of the given complex numbers. That is, for example, PQ = PO + OQ = OQ - OP = z₂ - z₁.

Multiplication of a vector by i produces a vector equal in length to the original and rotated by 90 degrees in an anticlockwise direction.

Thus, either PQ = iPR or PQ = iPR

 

[helpfulperson?]

I did try that but I still couldn’t get the correct answer

 

[axyx]

 

[appleali]

Express PQ and PR as vectors in terms of the given complex numbers. That is, for example, PQ = PO + OQ = OQ - OP = z₂ - z₁.

Multiplication of a vector by i produces a vector equal in length to the original and rotated by 90 degrees in an anticlockwise direction.

Thus, either PQ = iPR or PQ = iPR

Sorry to be a nerd but technically scaling vectors by complex is undefined, so you should set a variable for the vector and scale that by i.

 

[Luukas.2]

Sorry to be a nerd but technically scaling vectors by complex is undefined, so you should set a variable for the vector and scale that by i.

It is true that some aspects of vectors becomes problematic in complex numbers, which is an area that the HSC syllabus avoids, but the approach I have described is valid and the notation generally used.

 

[Trebla]

It is true that some aspects of vectors becomes problematic in complex numbers, which is an area that the HSC syllabus avoids, but the approach I have described is valid and the notation generally used.

I think what he means is that it is technically problematic/sloppy notation to multiply the vector by i (e.g. it is notationally problematic to say i*PQ) because you’re not actually multiplying the vector itself by a complex number. You’re actually multiplying the complex number representing the vector (note that a complex number does not equal at vector) with another complex number (e.g. should be written as say i*z).

It’s like how in an integral you always need the “dx” at the end to be technically precise. Whilst most people will generally get what you mean, it is just sloppy notation to omit it.

 

[appleali]

I think what he means is that it is technically problematic/sloppy notation to multiply the vector by i (e.g. it is notationally problematic to say i*PQ) because you’re not actually multiplying the vector itself by a complex number. You’re actually multiplying the complex number representing the vector (note that a complex number does not equal at vector) with another complex number (e.g. should be written as say i*z).

It’s like how in an integral you always need the “dx” at the end to be technically precise. Whilst most people will generally get what you mean, it is just sloppy notation to omit it.

Perfectly said