Hello guys.
I have a complex vector that starts at a+(jw)b and terminates at c+(jw)d

do i calculate the length and angle as following or do Complex vectors have their own special formulas

length=sqrt[(c-a)^2+(d-b)^2]

angle= arctan[(d-b)/(c-a)]

 

Hello guys.
I have a complex vector that starts at a+(jw)b and terminates at c+(jw)d

do i calculate the length and angle as following or do Complex vectors have their own special formulas

length=sqrt[(c-a)^2+(d-b)^2]

angle= arctan[(d-b)/(c-a)]

Not quite. You need to account for ω in your calculations.

\(L = \sqrt{(c-a)^2+(d\omega-b\omega)^2}\)

\(\angle=\arctan(\frac{d\omega-b\omega}{c-a})\)​

 

but w is not given

 

but w is not given

Then you cannot calculate a specific length. You can only say that length is a function of ω, or give the length for several values of ω. If ω=1 then your original formulation is correct. In which case you might want to rethink your original question. Does that help you?

 

OK here the problem attached

 

@Papabravo

 

OK here the problem attached

Right, I have the same book. I see an ω as a label for the imaginary axis,but that ω is not used in the evaluation of points in the complex plane. A general point is expressed as

a + jb, or c+jd​

and your original answer is correct.

 

OK but for the angle when s=-3+j4
I calculated the angle as theta =arctan[(4-0)/(-3-(-1))] i got -63.43 degree . how come???
@Papabravo

 

OK but for the angle when s=-3+j4
I calculated the angle as theta =arctan[(4-0)/(-3-(-1))] i got -63.43 degree . how come???
@Papabravo

The domain of the arctangent function is [-∞,+∞]
The range of the arctangent function is [-90°,+90°]
To get the postive angle you seek you need to add 180° to your result

-63.43° + 180° ≈ 116.6°​

Another way to look at it is that -63.43° is the angle from -3+j4 to the zero at -1+j0, while 116.6° is the angle from the zero at -1+j0 to the point a -3+j4
Does that clear things up?