HP 50g Graphing Calculator - Manual (Page 817)

Page C-6
It is recommended that you select EXACT mode as default CAS mode, and
change to APPROX mode if requested by the calculator in the performance of
an operation.
For additional information on real and integer numbers, as well as other
calculator’s objects, refer to Chapter 2.
Complex vs. Real CAS mode
A complex number is a number of the form a+bi, where i, defined by is
the unit imaginary number (electrical engineers prefer to use the symbol j), and
a and b are real numbers. For example, the number 2 + 3i is a complex
number. Additional information on operations with complex numbers are
presented in Chapter 4 of this guide.
When the _Complex CAS option is selected, if an operation results in a
complex number, then the result will be shown in the form a+bi or in the form of
an ordered pair (a,b). On the other hand, if the _Complex CAS option is unset
(i.e., the Real CAS option is active), and an operation results in a complex
number, you will be asked to switch to Complex mode. If you decline, the
calculator will report an error.
Please notice that, in COMPLEX mode the CAS is able to perform a wider range
of operations than in REAL mode, but it will also be considerably slower. Thus,
it is recommended that you use the REAL mode as default mode and switch to
COMPLEX if requested by the calculator in the performance of an operation.
The following example shows the calculation of the quantity using
the Algebraic operating mode, first with the Real CAS option selected. In this
case, you are asked if you want to change the mode to Complex:
1 2 − = i
2 2 8 5 −