Complex Number question help!! (1 Viewer)

[ledamn]

If anyone would like to try to solve these questions, then you're welcome!

2) If |z| = 1, where a is a positive number, show that:
a) arg(z+1) = 1/2argz Easy(done)
b) |z+1| = 2sin(arg(z-1))

6) On the Argand diagram, the points P, Q, and R represent the complex number p, q, & r respectively. If pq +iq +ir = 0, what triangle is PQR?

7) Find all possible values for z4 if z1= 1+i, z2=2+6i, z3=-1+7i and z4 forms a parallelogram.


Thanks everybody!

 

[Triage]

If anyone would like to try to solve these questions, then you're welcome!

2) If |z| = 1, where a is a positive number, show that:
a) arg(z+1) = 1/2argz Easy(done)
b) |z+1| = 2sin(arg(z-1))

6) On the Argand diagram, the points P, Q, and R represent the complex number p, q, & r respectively. If pq +iq +ir = 0, what triangle is PQR?

7) Find all possible values for z4 if z1= 1+i, z2=2+6i, z3=-1+7i and z4 forms a parallelogram.


Thanks everybody!

2B

RHS = 2sin(tan^-1(Y/X-1)

RHS^2 = 4sin^2(tan^-1(Y/X-1)

= 4 ( tan^2(tan^-1(Y/X-1)) * cos^2(tan^-1(Y/X-1)))

= 4((Y/X-1)^2 )* (1/1+(Y/X-1)^2))

 

[ledamn]

I don't understand what you did?

 

[Triage]

I don't understand what you did?

Nah I think I might be wrong.

Lets let Z = X + iY

therefor Z + 1 = X+1 + iY

yeah yeah yeah I see my mistake now.

so RHS^2 will equal 4sin squared of inverse tan of y/x+1

now sin squared can be re-written as cos squared + tan squared

thus tan^2 of the inverse tan of y/x+1 all multiplied by cos squared of the inverse tan of y/x+1

now cos^2 = 1/1+tan^2

 

[wiliaamnguuyen]

Yeah I think for 2B, it refers to the diagram in 2A

 

[Axio]

If anyone would like to try to solve these questions, then you're welcome!
6) On the Argand diagram, the points P, Q, and R represent the complex number p, q, & r respectively. If pq +iq +ir = 0, what triangle is PQR?
Thanks everybody!

Ok yeah I was wrong, I was doing it for pq + pr +qr = 0

 

[wiliaamnguuyen]

Nope, it's wrong. Question 6 is an isosceles right angled triangle at q. But I don't know how to show working out though

 

[wiliaamnguuyen]

I might be wrong, is it right @ledamn?

 

[ledamn]

Yeppe @Triage, I definitely think to get the solutions for 2B, you need the Argand Diagram on 2A.
Also quesiton 6 is difficult, don't know the answers tbh.

 

[ledamn]

Solutions to 2A

 

[ledamn]

nice

 

[actuallyapotato]

Is it too late to post a reply? I'm new and I don't know how long the appropriate timeframe to reply is.

I found 2B by using this Argand diagram



Then after messing with it a bit you'll find the angle between the lines representing z-1 and z+1 is 90 degrees, and you get the solution.

 

[ledamn]

Ah bro, that's still wrong LOL. I got the answer for every problem on top. If you guys want me to post it?

 

[Axio]

Ah bro, that's still wrong LOL. I got the answer for every problem on top. If you guys want me to post it?

Yeah sure