# Why some points do not satisfy the condition?

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Aisha Mohamed on 7 Apr 2023
Edited: John D'Errico on 7 Apr 2023
The following the projected curves (thanks to all experts) which represent discontinuty of the phase of this function
p = (-0.1540 + 0.2600*1i)+ ( 0.4347 + 0.0914*1i)*z+( 0.7756 - 0.4566*1i)*z.^2;
All the points $z=x + iy$ which lay on the projected curves must satisfy:,
when the polyval at $z = (x + iy)$ is calculated at these points, and then we calculate
the angle (polyval $(p, z))$ it must equal to $\pi$ or $-\pi$.
My question is:
Why some points on this curve (like z=-7373-0.07482i and z=0.3726-0.2577i) do not satisfy that:
angle (polyval $(p, z))$ it must equal to $\pi$ or $-\pi$.
I appriciate any help

John D'Errico on 7 Apr 2023
Edited: John D'Errico on 7 Apr 2023
So often this mistake is made. Are those the EXACT values of those coefficients? To me, that would seem a surprise, that they were estimated to EXACTLY 4 significant digits, when MATLAB does all of its computations in double precision, so roughly 16 significant digits. Hey. Anything is possible. Yeah, right. (There was some veiled sarcasm in there.)
Seriously, my point is, the coefficients of those curves are not exactly known. So you cannot expect an exact result from predictions made from those coefficients. And even at that, what you have is merely an approximation, a quadratic polynomial.
You need to remember these rules:
Rule 1: ALWAYS use the full coefficients, not a 4 digit approximation.
Rule 2: See rule 1.
As I said, this is a common mistake made, that you see 4 digits, so you assume that is all there is, forgetting that those lower order digits are actually important in what you must do.