difficult CN question (1 Viewer)

[shinn]

Been struggling with Part (iii),


Any help will be appreciated.

Thanks in advance,

 

[alcalder]

Can I humbly suggest using part ii and writing the thing in mod/arg form and then manipulating the trig functions (if you haven't done that yet)?

 

[Just.Snaz]

okay i did this thinking, no way in hell I'll get this cause I haven't done complex numberes in ages but my answers look believable so if right, I'll post up my answer..

z1 = -3/5 + 4i/5
z2 = 3/5 + 4i/5

 

[shinn]

so how did u end up getting those answers?

those are right though

p.s. i tried manipulating the trig and ended up with cos (b/2) =2 cos(a/2) and a+b = pi..... but im stuck here

 

[Just.Snaz]

so how did u end up getting those answers?

those are right though

p.s. i tried manipulating the trig and ended up with cos (b/2) =2 cos(a/2) and a+b = pi..... but im stuck here

from there make

b = pi - a

sub b into cos(b/2) = 2cos(a/2)

you'll end up getting a = 2 x inversetan2

then b = pi - 2 x inversetan 2

z1 = cis a
z2 = cis b

just type it into the calculator and yeah...

 

[shinn]

arghhhh im so stupid, thanks for pointing out my mistake

 

[Just.Snaz]

lol you're welcome

 

[tacogym27101990]

so i just found out i cant remember much about c.n
can someone give me a hint to the 1st part please??

damnitt i used to like complex numbers, i didnt think i'd forget it!

EDIT: don't worry my brain decided to work lol

 

[leisl1990]

i used a different approach.
change 2i into mudulus- argument form, then you have mudulus 2, argument pi/2
then you can equate the argument and mudulus in part ii with this.
solve them simultaneously, you should be able to get tan(alpha/2), then do a bit of trig, you can work out what sin and cos are.
then you can work it out in x+iy form.

z1=-3/5+4/5i, z2=3/5+4/5i
i am a bit dubious, coz i have two values for sine and cos, when i get tan.
you can do the calculation again, see if you can get this answer..

 

[Mark576]

i used a different approach.
change 2i into mudulus- argument form, then you have mudulus 2, argument pi/2
then you can equate the argument and mudulus in part ii with this.

It's ...modulus, not mudulus.

 

[leisl1990]

It's ...modulus, not mudulus.

thanks for pointing out my mistakes, i really thought it was mudulus..