Complex Numbers
You can carry out complex arithmetic
by choosing Complex mode from the Mode menu. If you select the Mode/Matrix
dialog and check the box to use arrays for all modes you can also work with
a one-dimensional array of complex numbers.
With complex numbers enabled, the column headings in the display are "x" and
"iy" to indicate the real and
imaginary parts of each number. On a desktop
PC, you may want to re-configure the keypads to a landscape layout for complex
number arithmetic, because of the extra width needed for the display. You can
then adjust the size of the display so that scroll bars are not needed.
You can perform simple arithmetic on
complex numbers, or perform exponentiation and logarithm functions and
transcendental functions. To enter numbers select the real or imaginary parts as
you would array elements as described in the section on
arrays and matrices. If you select the real or imaginary part of a complex
number, the arithmetic logic acts on the whole of the complex number, not just
the part selected.
You can carry out "normal" calculations on real numbers by setting the
imaginary part to zero. Of course in certain cases this may give rise to a
complex number, for example, famously:
Enter 1, then change its sign ("+/-"). Result:
Now take the square root. Result:
Basic complex arithmetic.
The arithmetic functions act in the same way as for real numbers. Complex
addition is the same as array addition, but multiplication and division are
slightly more complicated. For example:
(x1 + i.y1)(x2 + i.y2) = x1x2
+ i.x1y2 + i.x2y1
+ i 2.y1y2
= (x1x2 -y1y2) + i.(x1y2
+ x2y1)
Complex plane.
To convert from real and imaginary components to
modulus
and argument in the complex plane (Argand
diagram), use the normal r-p and p-r
buttons. These are obtained by using the shift key when they replace the "+" and
"-" arithmetic buttons. Once converted, the calculator does not "know" the
values are in polar co-ordinates, and you must convert back to Cartesian form to
continue calculations. The argument will be expressed in degrees, radians or
gradients depending on the angle mode selected.
Visualizing complex numbers in the complex plane is a powerful way of
thinking about the real and imaginary components of numbers. The behaviour of
arithmetic operations can be grasped more easily by considering the geometric
equivalents in the complex plane. For example, to take the square root of a
complex number, take the square root of the modulus and divide the argument by
two. You can verify this by using the calculator to take the square root of
various numbers and converting them to polar co-ordinates.
Logarithmic functions.
The logarithm, power and root functions are used in the same way as for real
numbers.
Trigonometric functions.
The trigonometric functions are used in the same way as for real numbers.