The principal branch used by the calculator for √ was chosen because it is analytic in the regions where the arguments of the real-valuedinverse 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 unit1 ⁄

2

 

 

'symb'

→

'

( symb)

'

 

SQ, ^, ISOL

 

 

 

See also:

 

 

 

 

 

 

 

 

 

 

 

 

Full Command and Function Reference 3-287