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Introduction to Complex Numbers
Friday, November 15, 2013
10:08 AM
Slides
Notes
Let's start with a quick review.
Saxon 2_ 3rd ed Page 1
Let's start with a quick review.
Imaginary numbers exist because you can
lose the information that a number under
the root sign was ever a negative. The
negative is replaced with an italic letter I,
called Euler notation. Imaginary numbers
get the name because you cannot actually
plot them on a number line.
Complex numbers are when you work
operation that include the imaginary
number in them. Here you can see the I
pop up with the 6i and the 3i. The terms
with imaginary numbers can be added
together but they cannot be added nor
subtracted to a number that doesn't have
an imaginary number.
What you are learning that is new in this
lesson is that when you have two
imaginary numbers, or you can just think
of it as two I's that are multiplied or an
exponent that is even, you can replace it
with a -1 for every pair of I's.
In this example, the -2 is replaced with 2 I
and the -3 with 3i because they are part of
a negative under a root sign.
When you continue by multiplying the
roots you get 6i-squared. There are two I's,
so you can replace the I with a negative 1.
Now remember that the I never was a
variable, it is Eluler's notation, so it doesn't
behave as a variable. When the squared I is
moved out from under the root bar
because this is a square root and any pair
can be pulled out front, you end up with a
negative 1 or more often it is just written
as a negative sign alone.
Saxon 2_ 3rd ed Page 2
Saxon 2_ 3rd ed Page 3