Sakigami's Questions Thread

[Sakigami]

Hi guys,
I'm having a bit of difficulty with Specialist at the moment, but hopefully someone will be able to help me and [when I get better], I'll be able to help others too. Haha. 

My question is:
Sketch in the complex plane {z: z = i*(conjugate of z)}.

[kamil9876]

so writing we want:





Which is equivalent to hence...

[Sakigami]

Ahh, that makes sense.
The imaginary component of the equation confused me. ^^;; Thanks kamil.

[Sakigami]

I have another question;
Prove that for any complex number z, 3|z − 1|2 = |z + 1|2 if and only if |z − 2|2 = 3.
Hence sketch the region S = {z: (3)^(1/2) |z − 1| = |z + 1|}.

[kamil9876]

I'm assuming those 2's on the end are squares.

Again just write , expand out and simplify. We get:













but notice that hence we are done.

[Sakigami]

It's been awhile! But here's another question related to Trig Identities, hoping someone can answer. =)

[brightsky]

i'll just use a and b.
(sec^2(a) (tan(b) + cot(b)))/(sec^2(b) (tan(a) + cot(a))
= (cos^2(b) (tan(b) + 1/tan(b)))/(cos^2(a) (tan(a) + 1/tan(a)))
= (cos^2(b) (tan^2(b) + 1)/tan(b))/(cos^2(a) (tan^2(a) + 1)/tan(a))
= (cos^2(b) (sec^2(b)/tan(b))/(cos^2(a) (sec^2(a)/tan(a))
= tan(a)/tan(b)
= cot(b) tan(a)

[Sakigami]

Ahhh, wouldn't have thought of rearranging it that way.
Thanks for the help brightsky! 

I also have another question...
Question asks you to "Simplify".

[brightsky]

2tan(2t)/(1+ tan^2(2t))
= 2tan(2t)/(sec^2(2t))
= 2tan(2t)cos^2(2t)
= 2cos^2(2t)sin(2t)/cos(2t)
= 2sin(2t)cos(2t)
= sin(4t)

[Sakigami]

Thanks again brightsky