Reference Guide

Full Command and Function Reference 3-135
For x = 0 or (0, 0), an Infinite Result exception occurs, or, if flag –22 is set, –MAXR is returned.
The inverse of EXP is a relation, not a function, since EXP sends more than one argument to the
same result. The inverse relation for EXP is the general solution:
LN(Z)+2*π*i*n1
The function LN is the inverse of a part of EXP, a part defined by restricting the domain of EXP
such that: each argument is sent to a distinct result, and each possible result is achieved.
The points in this restricted domain of EXP are called the principal values of the inverse relation.
LN in its entirety is called the principal branch of the inverse relation, and the points sent by LN to
the boundary of the restricted domain of EXP form the branch cuts of LN.
The principal branch used by the calculator for LN 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 natural log 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 LN. 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 LN(Z)+2*π*i*n1 for the case n1=0. For other values of
n1, the horizontal band in the lower graph is translated up (for n1 positive) or down (for n1
negative). Taken together, the bands cover the whole complex plane, which is the domain of
EXP.
You can view these graphs with domain and range reversed to see how the domain of EXP is
restricted to make an inverse function possible. Consider the vertical band in the lower graph as the
restricted domain Z = (x,y). EXP sends this domain onto the whole complex plane in the range
W = (u,v) = EXP(x,y) in the upper graph.
Access: …¹ (¹is the right-shift of the Qkey).
Flags: Principal Solution (–1), Numerical Results (–3), Infinite Result Exception (–22)