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1. finding the midpoint of 2 complex numbers
hi,

if i've got complex number a: root2 e^jpi/4
complex number b: root2 e^7jpi/12

i know that the argument of the mid point will be the average of the angles but how do i find the modulus?

thanks
2. Re: finding the midpoint of 2 complex numbers
bump
3. Re: finding the midpoint of 2 complex numbers
The argument of the midpoint will not (in general) be the average of the angles. but it will be in this case because the numbers have the same modulus.

The general way of doing this is to convert to Cartesian form (x+iy) for both numbers, then you simply add them add divide by two (and then convert back to polar form if needed).

In your particular case, it may be slightly easier to do something geometrical, but I'm not sure I'd bother.
4. Re: finding the midpoint of 2 complex numbers
(Original post by DFranklin)
The argument of the midpoint will not (in general) be the average of the angles. but it will be in this case because the numbers have the same modulus.

The general way of doing this is to convert to Cartesian form (x+iy) for both numbers, then you simply add them add divide by two (and then convert back to polar form if needed).

In your particular case, it may be slightly easier to do something geometrical, but I'm not sure I'd bother.
thanks a lot
5. Re: finding the midpoint of 2 complex numbers
I would convert to x+yi form, draw on an argand diagram, and try and work it out geometrically. Just 'cause I find it easier to visualise things
6. Re: finding the midpoint of 2 complex numbers
(Original post by DFranklin)
The argument of the midpoint will not (in general) be the average of the angles. but it will be in this case because the numbers have the same modulus.

The general way of doing this is to convert to Cartesian form (x+iy) for both numbers, then you simply add them add divide by two (and then convert back to polar form if needed).

In your particular case, it may be slightly easier to do something geometrical, but I'm not sure I'd bother.
I think I'm running a great risk by disagreeing with DF, but isn't the trig here so simple that you can guess that's the intended method?
7. Re: finding the midpoint of 2 complex numbers
(Original post by ian.slater)
I think I'm running a great risk by disagreeing with DF, but isn't the trig here so simple that you can guess that's the intended method?
I can't see it without actual calculation, but this certainly doesn't mean I'm right. Does it work out nicely?

[Neglecting that I'd rather someone learns a "not neat" method that always works, rather than believing that you can "average" the arguments...]
8. Re: finding the midpoint of 2 complex numbers
(Original post by DFranklin)
I can't see it without actual calculation, but this certainly doesn't mean I'm right. Does it work out nicely?

[Neglecting that I'd rather someone learns a "not neat" method that always works, rather than believing that you can "average" the arguments...]
I confess I didn't do the calculation, but in my 'mental diagram' I could see equal moduli, arguments differ by pi/3; OP wants answer in modulus/argument form so cos (pi/6) looks helpful ..
9. Re: finding the midpoint of 2 complex numbers
(Original post by ian.slater)
I confess I didn't do the calculation, but in my 'mental diagram' I could see equal moduli, arguments differ by pi/3; OP wants answer in modulus/argument form so cos (pi/6) looks helpful ..
Yeah, I suspect you're right. Apologies to the OP.