complex numbers (1 Viewer)

[redslert]

when the question asks you to find the locus of something
like |z -2|=2

it's a circle...

you sketch the graph of the circle and then you write a small sentence saying that the locus of P is the circle centre (2,0) radius 2

do you have to write down the equation of the circle? i know this one isn't hard but there are harder ones....
also if i do have to write the equation, do i have to show working out, if i just do it from the sketch?

you know what i mean??

 

[MyLuv]

Originally posted by redslert
do you have to write down the equation of the circle?

No

 

[Fosweb]

If the question is that simple, and worth 2 marks or whatever, then I would just be subbing z = x+iy into that, taking mod and that way you have the equation in only a couple of lines anyway...

I usually do that for all those questions. Doesnt take too long.

 

[ND]

If it asks you to find the locus, there's no point drawing it. On a simple one like that just state that it's a circle with centre (2,0) and radius 2. For lines or more complex ones (like hyperbolas or something) write out the cartesian equation, but most of teh time there's no need to let z=x+iy, you can usually tell by looking at it.

 

[redslert]

ok thankz!

also another question

when the question asks to express say 'z' in modulus -argument form

how would you leave your answer?

r.cis.@
OR
r[cos@+i.sin@]

because i usually use cis but in the solutions of my past-papers they use cos and sin????
and sometimes when @ is negative they would change things around, but if i use cis...i can't do that???

 

[stag_j]

both will be ok
and if @ is negative, you can still write cis(-pi/3) etc
which is easier in some ways because if you write it as cos(pi/3) - i.sin(pi/3) then i find i sometimes forget about the negative sign and end up getting a wrong answer

 

[Fosweb]

for some things though, esp if they throw you a q7/8 on polynomials/complex numbers, you may need the result that cos(-@) + isin(-@) = cos@ - isin@