Basic Complex number algebra (1 Viewer)

[Dumbledore]

i've read a few threads on complex numbers here and found that either
1: i slept in class without knowing (hopefully not) or
2: my teacher skipped a whole section on it

how do you do basic algabraic laws on mod-arg form complex numbers

e.g arg(z1/z2) can this be simplified into something like arg(z1)-arg(z2) [what i've gather from reading other posts]
can stuff like re(z1/z2) or re(z1-z2) or arg(z1/z2)or arg(z1-z2) be simplified/changed

when i've come across question like sketch arg[(z+1)/(z-1)]=pi
and sketch arg(z-1)+arg(z+1) = pi/4 (something like that)
i've been stumped on how to manipulate it

plz post up any other mod-arg algebra i might have missed
ty in advance

 

[ibrian]

arg(z1/z2) = arg(z1)-arg(z2)
thats one of a few laws but they kinda straight forward. are you asking for the list of laws or how to prove them?

and for sketching arg[(z+1)/(z-1)]=pi u use the laws like you said and change it in the form ==> arg(z-1)+arg(z+1) = pi/4 and sketch each argument seperatly on an argand diagram and the angle btwn them is pi/4, but be careful of which circle to shade in (i think, im kinda rusty on complex)