# Trignomometric Modes; Definitions Of Math Functions - HP -15C Advanced Functions Handbook

68
Section 3: Calculating in Complex Mode
Keystrokes
Display
-6.130324145
Real part of ln(F(l + 5i)).
3.815898575
Imaginary part of
ln(r(l + 5/)).
3.8159
The complex result is calculated with no more effort than that
needed to enter the imaginary part of the argument z. (The result
ln(F(l + 5i)) has 10 correct digits in each component.)
Trigonometric Modes
Although the trignometric mode annunciator remains lit in
Complex mode, complex functions are always computed using
radian measure. The annunciator indicates the mode (Degrees,
If you want to evaluate re
l6
where 6 is in degrees, [e*l can't be used
directly because 6 must be in radians. If you attempt to convert
from degrees to radians, there is a slight loss of accuracy,
especially at values like 180° for which the radian measure -rr can't
be represented exactly with 10 digits.
However, in Complex mode the L^R | function computes re
ie
accurately for 6 in any measure (indicated by the annunciator).
Simply enter r and 6 into the complex X-registers in the form r + id,
then execute |+R | to calculate the complex value
re
lB
= r cos 9 + ir sin 9.
(The program listed under Calculating the nth Roots of a Complex
Number at the end of this section uses this function.)
Definitions of Math Functions
The lists that follow define the operation of the HP-15C in Complex
mode. In these definitions, a complex number is denoted by
z = x + iy (rectangular form) or z = re
ie
(polar form). Also
M=
v/
?+7.  