Maths quiz

[Grisu]

uhh, it's been a while but i will try to answer it:

z3 = z1/z2= 1/|z2|^2 * z1*z'2= 1/16 * (sqrt(3) + i)*(sqrt(8) - sqrt(8)*i) = sqrt(8)/16 * (sqrt(3) +1) + (1-sqrt(3)i

|z3|= sqrt((sqrt(8)/16)^2(3 + 2sqrt(3)+ 1)+(1 - 2sqrt(3) + 3)) = 1/2

hope this is correct.

i have forgotten how to do the exponential form though, i have gotten a result with my calculator but I'll leave that to someone who manages it without help.

 

[Lucky]

The general formula you chose is correct, but the harder way to do it!

But your calculation for z3 wrong.
Yyou forgot the minus´ in front of the real terms of BOTH z1 and z2.
The absolute value is correct though. But the imaginary term consequently has the wrong sign.

To calculate the phase f you have to remember some other formulas.

z=a+ib=|z|*(cos f + i*sin f)=|z|*e^if
|z|=SQRT(a^2+b^2) f=arctan(b/a)

So now it should only be a matter of calculation it right.
Of course calculators are allowed, I don´t think anyone here is able to calculate the arctan of something and only a few might be able to take squareroots in the head.
The numbers I chose are somewhat easy though.

Only the phase angle f and the expontial form is needed now! All formulas above. But please also some solution steps, not only results.

 

[Grisu]

So if nobody else wants it i'll give it a 2nd try (this time with the correct signs (i do this all the time...).

so the correct term for z3 should be sqrt(8)/16 *((1 - sqrt(3)) + (sqrt(3) + 1)i) hope it is correct now.

using your formula for the phase (how did you make that sign?): phase=arctan((sqrt(3)+1)/(1-sqrt(3))+pi -> a is <0 therefore you have to add pi (or 180 degrees). so the result for the phase is 7pi/12 or 105°.

So the polar-Form is 1/2 * (cos(7pi/12) +i*sin(7pi/12))= 0.5*e^(7pi/12)i

hope I didn't mess it up again

of course I did the arctan with my calculator, what I meant earlier was that I entered the carthesian form and got the exponential one, so there was not be much thinking included.

 

[Grisu]

upps, I think I DID mess it up again. I found an my math book and did try the division the easy way: z1/z2 = |z1|*|z2|*e^i(phase1-phase2).

|z1|=sqrt(sqrt(3)^2 + 1^2) = 2, |z2|=sqrt(sqrt(8)^2 + sqrt(8)^2) = 4

phase1=arctan(1/-sqrt(3))=-pi/6+pi = 5pi/6
phase2=arctan(sqrt(8)/-sqrt(8))=-pi/4+pi = 3pi/4
phase3=phase1-phase2= pi/12 = 15°

z3 = 1/2 * e^i(phase1-phase2) = 1/2 * e^i(pi/12)

so now THIS should be correct.

 

[Lucky]

Yes!

Phase is 15° and the absolute value 1/2.

--> z3 = 1/2 * e^i*15° (pi/12)

So you are correct, your turn Käptn!

 

[Ohkrana]

Are you people Kreyzig readers?

Good to see some maths buffs out there.

As for the poster terming you nerds; some of us are numerate. Therefore we have a life.

My questions is probably a bit unfair,but I'm not a fair minded kind of guy.

The Intergral of (Dn/Cabin) = ???

So take a shot, see what you come up with.

Might get 'nasty' and go with some DE's next

Maths as easy as 3.1412857......

 

[Grisu]

Actually it would be my turn

but it's ok, you can have it, I wouldn''t know what to ask anyway.

but your question is somewhat beyond me: what is Dn or Cabin?

 

[Lucky]

Never heard of these terms either.

AND READ THE RULES!

Only if you answer a question correctly you can post the next one!!!

But since Käptn doesn´t mind, care to explain what you mean by your question?

 

[Ohkrana]

I apologize for jumping the queue, I should no better.

Wonder what the probability is on queue jumping? If only I could find my Markov chains.

It was actually a maths joke and the only one I found funny in my maths courses.

Integral (Dn/Cabin) = Log(Cabin) + C

I figured you maths buffs would get a kick out of it.

So Ovi have your turn back, I don't want to be a queue jumper mate.

*Ohkrana - just trying to get along with everyone till the time is right*

 

[Lucky]

Hey KaeptnOvi, how about posting the next question?

I´m eagerly waiting and so are others.

 

[Grisu]

okay you wanted it this way! i just took the first question in mind:

what is the inverse matrix A^-1 of the fallowing matrix A = [cos(phi) sin(phi); -sin(phi) cos(phi)]
the semicolon separtes the rows

 

[AVN]

The determinant = cos(phi)^2+sin(phi)^2=1

A^-1 = 1/det [cos(phi) -sin(phi) ; sin(phi) cos(phi)]
= [cos(phi) -sin(phi) ; sin(phi) cos(phi)]

 

[Grisu]

correct, your turn :welldone:

 

[AVN]

Because Ohkrana started the calculus quiz, which I consider to be a new math quiz, this thread can be closed ?

 

[Lucky]

No, Ohkrana started a Calculus quiz, only for actual calculation but not including things like geometry.

And his thread was started later, so that one should be closed.

Post your question.

 

[Baleog]

I think the method involving differenciation which allhailindia was reffering to way back on page 1 was teh Method of Lagrange Multipliers. Was this mentioned? I only skitted through the first pages so somebody may have mentioned this all ready.