A point in the complex plane with both coordinates rational is called a rational point. The set of rational points on the unit circle will be denoted by C(Q): C(Q) = {a + bi ∈ C | a, b ∈ Q, and a^2 + b^2 =1}. A triple (a,b,c), where a, b, and c are integers, c ̸= 0, and a^2 + b^2 = c^2 is called a Pythagorean triple. When do two different Pythagorean triples give the same element of C(Q)?

A point in the complex plane with both coordinates rational is called a rational point. The set of rational points on the unit circle will be denoted by C(Q): C(Q) = {a + bi ∈ C | a, b ∈ Q, and a^2 + b^2 =1}. A triple (a,b,c), where a, b, and c are integers, c ̸= 0, and a^2 + b^2 = c^2 is called a Pythagorean triple. When do two different Pythagorean triples give the same element of C(Q)?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter12: Conic Sections

Section12.1: Parabolas

Problem 1E: A parabola is the set of all points in the plane that are equidistant from a fixed point called the...

See similar textbooks

Similar questions

A parabola is the set of all points in the plane that are equidistant from a fixed point called the ______ and a fixed line called the _______ of the parabola.
Provide Solution of the Equation by appliying Wronskians of Solutions theorem?
Find the number of points in the xy-plane with integer coordinates located at a distance 5 from the point (4, 2)
If l is a line through (0,0), the point (0,0) divides the line l into two rays. Also, a complex-valued function g on a set S is said to be bounded if there is some finite M such that |g| < M on the set S. So we need to find out for which rays through the origin does e^z satisfy this property.
Can you help me to show that the systhem has a unique solution.
A quadrilateral has coordinates R(-5,2) , S(-1,3) , T(-2,-1) and U(-6,-2). Verify algebraically, that the midsegments of the quadrilateral form a rectangle.
What is the image of the point (3,-6) after a rotation of 90° counterclockwise about the origin?
Sketch the regions in the complex plane and state whether they are: open, closed, neither, path crossed.
Give the coordinates of the harmonic conjugate of (–1, –1, 0) with respect to (1, 1, 1) and (3, 3, 1).
If the origin is shifted to the point (–2, 3) and the new co-ordinate axes are parallel to the original ones, the co-ordinates of (3, 5), is (–5, 2) (5, 2) (5, –2) (–5, –2)
Determine the vertical traces of elliptic and parabolic cylinders in standard form.
Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.)