Complex Numbers
The graphing calculator can be a very
useful tool for checking your work with complex numbers.
Keep in mind, when working with a graphing
calculator, that there may be more than one way
to arrive at an answer.

Use the MODE key
to place
the
calculator in a+bi mode.

The
complex i is found
above the
decimal point key or in the catalog.

Note: Complex numbers can be
accessed from Real Mode (without placing calculator in a + bi Mode).
Real mode, however, does not display complex results unless complex
numbers are entered as input. For example, if the calculator is NOT
in a + bi Mode,
will create an error.
You get an error message when you try to enter the square root of a
negative number when in Real Mode. 
You need to be in a + bi mode to
evaluate the square root of a
negative number. 
Now, let's look
at the arithmetic of complex
numbers:
Add:
(2 +
4i) + (3  2i) 
Subtract:
(6 
3i)  (4 + 5i) 
Multiply:
(3 +
2i) (4  2i) 



Divide : (2+3i)/(43i)
(answer appears in a + bi form) WOW!!
The calculator did the conjugate work for you.

For TI83+ and for TI84+ with OS prior to
OS 2.53MP.
In this display, i is NOT in the denominator! The
calculator is simply listing order of operations.

TI84+ with OS 2.53MP

Be careful to write your final answer correctly.
Note the location of the i in the final answer:
NOTE: On OS2.53MP, if the decimals you are trying to "grab" to convert to fractions are really long, use
MATH  CPX  real( and imag( to "grab" the full decimal value for converting "a" and "b" to fractions.

Using the calculator to investigate powers of
i:
Investigate
the powers of i.


These values
will appear when you are in either
Real Mode or
in
a + bi mode. 
You can look at many powers at once by using a list

...
use right arrow to scroll to the right to see all of the answers

What kind of number is
 3E  13  i
???
This number is really just
 i.
 3E  13
is so small, it is considered to be
zero.
(E13 is Scientific Notation meaning 10 raised to 13
power.)


"My Deer, BEWARE!!!
When raising i to a power on a
graphing calculator, accuracy diminishes as the powers increase.


There are also special functions on the
graphing calculator to deal with complex numbers (but you probably won't
need a calculator for many of these functions):

1. conj(
returns the complex conjugate of a complex number.
conj(2+5i)
gives 25i
2. real( returns the "a"
value in an a+bi complex number.
real(2+5i)
gives 2
3. imag( returns the "b"
value in an a+bi complex number.
imag(2+5i)
gives 5 
5. abs(
returns the absolute value of the complex number.
abs(5+12i) gives
13
(Note: The
absolute
value of a complex number may also be called its magnitude.
It you plot a complex number as a single point, the absolute value
represents the distance from the origin to that point. If you
plot a complex number as a vector, the absolute value represents the
length of the vector.) 
BACK
