My Math Forum To find a system of coordinates for visualise a system of equations

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 August 28th, 2015, 04:33 PM #1 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 To find a system of coordinates for visualise a system of equations Given a system of equation (and its inverse): $A= \frac{\alpha + \beta}{2}$ $B= \sqrt{\alpha \beta}$ $\alpha= A + \sqrt{A^2-B^2}$ $\beta= A - \sqrt{A^2-B^2}$ Which is the best system of coordinates (not necessarily orthogonal) that represents graphically these equations? OBS: A is a real number (... -3, -2, -1, 0, 1, 2, 3 ...) B is a POSITIVE real number or is a POSITIVE imaginary number (... i3, i2, i1, 0, 1, 2, 3 ...) Last edited by Jhenrique; August 28th, 2015 at 04:36 PM.
 August 29th, 2015, 06:33 AM #2 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 By geometric interpretation of geometric and arithmetic means, I concluded that A = x and B = r. This works very well! Using the relationship r² = x² + y², I concluded that α = x + i |y| β = x - i |y| Can you help me with this interpretation? Generally, complex numbers are defined like x + i y (without absolute!) Why the variable y appears inside of absolute function in this formula? And how I can understand the values of r? Since r is a positive real number or a positive complex number! OBS: r² = x² + y² r² - x² = y² √(r² - x²) = √(y²) √(r² - x²) = |y| Last edited by skipjack; August 29th, 2015 at 11:15 AM.

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