MathBIts.com  Table of Contents
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)/(4-3i)
(answer appears in a + bi form)   WOW!!
 The calculator did the conjugate work for you.

Be careful to read this answer correctly. 
The calculator is telling you that the answer is

(i is NOT in the denominator!  The
calculator is listing order of operations.)

 

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.
(E-13 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  2-5i

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.)


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