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Related to radicand: Principal square root

(mathematics)
The quantity that appears under a radical sign.
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where w([[eta].sub.2]; [gamma]) = [square root of [([[eta].sup.2.sub.2] + [[kappa].sup.2.sub.2]).sup.2] + 2[[beta].sub.2] [C.sub.2] and the radicand is positive for all real [[eta].sub.2] and [gamma].
It can guarantee that the radicand and root number found are minimum.
Equating expressions (8) and (10) one gets a second order equation for [beta]: 0 = - [[beta].sup.2] + (1 - r) [beta] + (r - [gamma]/y) where the roots ([[beta].sub.inf], [beta].sub.sup]) are given by (16), whose radicand is always positive, since from proposition 7 and expression (11), there is an intersection between the two locus when r [greater than or equal to] r*.
The phase constant [beta] can be purely real or purely imaginary depending on whether the radicand is positive or negative, respectively.
However, they cannot be obtained for a precious few complex loads because the radicand in [X.sub.p] and [X.sub.q] should be always a positive value in (13), (18).
To this end, let us find out the derivative of the radicand and set it to zero.
That is, students may recognize the negative radicand in the standard deviation calculation, but not easily determine why it is negative.

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