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August 28th, 2015, 04:33 PM   #1
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To find a system of coordinates for visualise a system of equations

Given a system of equation (and its inverse):










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.
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August 29th, 2015, 06:33 AM   #2
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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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