HP 50g User's Reference Manual
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Brand: HP
Category: Calculator
Type: Advanced user's reference manual
Model: HP 48gII , HP 49g+ , HP 50G
Pages: 693
Full Command and Function Reference 3-287
The principal branch used by the calculator for √ was chosen because it is analytic in the regions
where the arguments of the real-valued inverse function are defined. The branch cut for the
complex-valued square root function occurs where the corresponding real-valued function is
undefined. The principal branch also preserves most of the important symmetries.
The graphs below show the domain and range of √. The graph of the domain shows where the
branch cut occurs: the heavy solid line marks one side of the cut, while the feathered lines mark
the other side of the cut. The graph of the range shows where each side of the cut is mapped
under the function.
These graphs show the inverse relation 's1*√Z' for the case s1=1. For the other value of s1, the
half-plane in the lower graph is rotated. Taken together, the half-planes cover the whole complex
plane, which is the domain of SQ.
View these graphs with domain and range reversed to see how the domain of SQ is restricted to
make an inverse function possible. Consider the half-plane in the lower graph as the restricted
domain Z = (x, y). SQ sends this domain onto the whole complex plane in the range W = (u, v) =
SQ(x, y) in the upper graph.
Access: R
Flags: Principal Solution (–1), Numerical Results (–3)
Input/Output:
Level 1/Argument 1 Level 1/Item 1
z
→
z
x_unit
→
x
u
n
i
t
1
2
⁄
'symb'
→
'
symb( )
'
See also: SQ, ^, ISOL