4Units Problem-Solving section (2 Viewers)

[Grey Council]

A problem for Victorling. For victorling, mind. hehe, i'll ask everyone else later, first give victorling a chance.

Find the complex number z with the lest positive argument satisfying the condition
| z - 25i | =< 15 __( in other words, modulus of z-25i is less than or equal to 15)

have fun!

 

[KeypadSDM]

Dude, so easy man. Can't I just answer it now?

 

[victorling]

can anybody help me to reduce the size of the graph?
it is way too big!!!800kb, while it allows only 100kb
i used paint

 

[Grey Council]

damn it, thats supposed to be hard! wtf, this is depressing. humph

hehe, victorling learnt to save in jpg format. it went from 800kb to 20kb. lol

 

[KeypadSDM]

Dude, the question is astoundingly easy. Maybe you were attacking it the wrong way?

To size it down use jpeg format not BMP

 

[victorling]

Originally posted by Grey Council
A problem for Victorling. For victorling, mind. hehe, i'll ask everyone else later, first give victorling a chance.

Find the complex number z with the lest positive argument satisfying the condition
| z - 25i | =< 15 __( in other words, modulus of z-25i is less than or equal to 15)

have fun!

 

[victorling]

Use 15/25 = sin(alpha)

then alpha can be evaluated, which is....36.86989765 degrees, better change it into minute and second

then the least positive argument is 90-36.86989765=53.13010235degrees

 

[Grey Council]

whooops.

find the complex number, not the argument.

 

[KeypadSDM]

That's easy enough. Foo.

12 + 16i

I hope. (I pray to god nightly)

 

[Grey Council]

thats right

now i'd like to see how you did it. I can't do it.

 

[victorling]

the modulus of the complex number we want = sqrt(25^2-15^2)=20
the argument is 53.13 degress
therefore the answer is 20cis(53.13degrees), better change the degree into minute and second...

 

[victorling]

expanding the 20cis(53.13) gives u 12+16i

 

[KeypadSDM]

And you will also note that Tan^-1(4/3) gives you the required angle as well. Implying that the coordinates must be of the form 3a + 4ai

 

[victorling]

yep
cool^_^

 

[KeypadSDM]

Question.

Prove that all even numbers
n >= 6 (n <> 10) can be represented in the form:

p1 + p2p3

Where p1, p2, and p3 are primes.

 

[victorling]

what is the relationship between p1,p2 and p3

 

[KeypadSDM]

p1 + p2 * p3 = n
Where n E Z
n/2 E Z
n >=6
n <> 10

 

[Grey Council]

hokay, use victorling's diagram. we know |z| is 20 and we know theta. bring down a line from the point of contact parallel to the imaginary axis till it touches the real axis. You now have another right angled traingle. use r cos theta and r sin theta to find the coordinates.

 

[victorling]

sorry...keypad
didn't concentrate on the question u asked
damn msn!

 

[J0n]

Originally posted by KeypadSDM
Question.

Prove that all even numbers
n >= 6 (n <> 10) can be represented in the form:

p1 + p2p3

Where p1, p2, and p3 are primes.

Can't you just let p1 = 2 and say that p2*p3 can be represented by the product of two primes by the fundamental theorem of arithmetic? or am i horribly wrong, cause it seems too easy