Finding trigonometric forms.

Find the trigonometric form of the complex number where 0 <= theta < 2pi on the equation: r= 1/2 - [(sqrt(3)/2)i]

Working with sequential ambiguity.

In a specific sequence to create, a1 has the elements x1 and y1, a2 has the elements x2 and y2, a3 has the elements x3 and y3, The relationship between each term cannot be bijective, however it has a bounded range of finite whole numbers. Create a rule such that f(x1,y2)=x2 and f(x2,y3) = x3. The rule must be such that after the sequence has been created, if you are given x3,y3,x2 and y1, then x1 and y2 can be determined i.e y2 = g(x2,x3)

Sequential Ambiguity

On Monday, May 26th/03, I posted the following question to which a solution was provided by Remus Nicoara, PhD (IP). I thank Remus for his assistance and solution. I'm interested in knowing what the solution would look like if for each term, the y elements are randomly determined. Original Question In a specific sequence that I am to create, a1 has the elements x1 and y1, a2 has the elements x2 and y2, a3 has the elements x3 and y3, The relationship between each term cannot be bijective, however has a bounded range of finite whole numbers. I am to create a rule such that f(x1,y2)=x2 and f(x2,y3) = x3. The rule must be such that after the sequence has been created, if I am given x3,y3,x... click for more

Proof of the Irrationality

2. Apply the proof of the irrationality of sqrt(2) to a) sqrt(3) and b) sqrt(4). If the proof breaks down, indicate precisely why. 3. Euler's phi-function is defined such that for n > 0, phi(n) = |{m < n: gcd(m,n)=1}|. So, e.g., phi(4) = |{1,3}| = 2; phi(5) = |{1,2,3,4}| = 4. a. Show that for prime p, phi(p) = p-1. b. Show that for prime p and q, phi(p*q) = (p-1)*(q-1).

Working with Pythagorean triples.

Find a pythagorean triple with sides (x^2)-1, (y^2)-1, (z^2)-1, where x,y,z are integers.