forgot how to do easy proving in complex number :( (1 Viewer)

[coeyz]

prove :

argz1 - argz2 = arg (z1/z2)

anyone please help~~?
thankss

 

[coeyz]

arg (z-1 / z+1) = pie/2

find the locus of the point which represents z

and also this question thanks

 

[Timothy.Siu]

arg (z-1 / z+1) = pie/2

find the locus of the point which represents z

and also this question thanks

its a semi circle origin at the centre and radius 1 above the x axis (so 1,0 and -1, 0 are circled)

 

[GUSSSSSSSSSSSSS]

for the first:
divide z1 by z2 where z1=cos(n) + isin(n)
z2=cos(m) + isin(m)

realise the denominator
group into real nd imaginary
and then its just a compound angle formula job
(sorry bout all the shitty notation)


the second one end up as a semicircle

i cbb to explain at the moment sorry someone else will lol

 

[coeyz]

thanks guys

for the first one,
ye i did the way u said,
but and then i get

z1/z2 = r1/r2 cis (日1-日2)

then i can only say arg(r1/r2) = 日1-日2

 

[GUSSSSSSSSSSSSS]

thanks guys

for the first one,
ye i did the way u said,
but and then i get

z1/z2 = r1/r2 cis (日1-日2)

then i can only say arg(r1/r2) = 日1-日2

sorry i dun get ur notation

but up the begining where u defined r1 and r2 you gave their arg
then you can just replace that again down the bottom
if you get wat i mean??????

 

[coeyz]

z1/z2 = r1 (cosN+isinN) (cosM-isinM)
r2 (cosM+isinM) (cosM-isinM)

= r1 cos (N-M) - isin(N-M)
r2

= r1 cis (N-M)
r2

then?

 

[lolokay]

arg(z1/z2) = 日1-日2
arg(z1/z2) = arg(z1) - arg(z2)

 

[GUSSSSSSSSSSSSS]

z1/z2 = r1 (cosN+isinN) (cosM-isinM)
r2 (cosM+isinM) (cosM-isinM)

= r1 cos (N-M) - isin(N-M)
r2

= r1 cis (N-M)
r2

then?

yea exactly as the guy above me said
r1=cosN+isinN
so arg(r1)=N
similarly for r2
so arg(r1/r2)=N-M=arg(r1)-arg(r2)

 

[shuning]

sif not helping me Angus T.T

 

[GUSSSSSSSSSSSSS]

sif not helping me Angus T.T

hahahahaha do you need help????????

your good enuf rnt you hehe

 

[coeyz]

oh i got it now
thanks everyone!

 

[shuning]

hahahahaha do you need help????????

your good enuf rnt you hehe

cant u see my thread right below this 1 LOL