HP 15c - Manual (Page 58)

58 Section 3: Calculating in Complex Mode
58
Keystrokes Display
195 v371÷ 0.5256
O4 0.5256 Stores a
4
.
1.011523068
O5 1.0115 Stores a
5
.
1.517473649 O6 1.5175 Stores a
6
.
Use this program to calculate ln(

(4.2)), then compare it with ln(3.2!) calculated with the
! function. Also calculate ln( 
(1 + 5i)).
Keystrokes Display
4.2 ´A 2.0486
Calculates ln(

(4.2)).
´•9 2.048555637 Displays 10 digits.
3.2
´! 7.756689536
Calculates (3.2)! =

(3.2+1).
|N 2.048555637 Calculates ln(3.2!).
1 v 1.000000000 Enters real part of 1 + 5i.
5
´V 1.000000000 Forms complex number
1 + 5i.
´A -6.130324145
Real part of ln(

(1 + 5i)).
´} 3.815898575 Imaginary part of
ln(

(1 + 5i)).
´•4 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(

(1 + 5i)) has 10 correct digits in each component.)
Trigonometric Modes
Although the trigonometric mode annunciator remains lit in Complex mode, complex
functions are always computed using radian measure. The annunciator indicates the mode
(Degrees, Radians, or Grads) for only the two complex conversions: : and ;.
If you want to evaluate re
i

where

is in degrees, ' can't be used directly because

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

can't be represented
exactly with 10 digits.
However, in Complex mode the ; function computes re
i

accurately for

in any measure
(indicated by the annunciator). Simply enter r and

into the complex X-registers in the form
r + i

, then execute ; to calculate the complex value
re
i

= r cos

+ ir sin

.
(The program listed under Calculating the n th Roots of a Complex Number at the end of this
section uses this function.)