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Imaginary Numbers ???
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In real life, complex numbers are used by
engineers and physicists to measure
electrical currents, to analyze stresses in
structures such as bridges and buildings,
and to study the flow of liquids.
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Engineers who design speakers use
complex numbers.
Engineers who design and test the
strength of bridges use complex numbers.
Scientists who do experiments on ways to
make energy using fuel cells, batteries,
and solar cells use complex numbers.
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Complex numbers are also used for
generating fractals, which are geometric
objects created by making a repeating
pattern.
Which is actually very useful
because…
…by simply accepting that i exists
lets us solve things where we need
the square root of a negative
number.
Example: What is the square root of -25?
Answer:
 25  25   1  5i
A few questions…

Simplify

A)
9
B)
2  48
i0  1
i4  1
i8 
i1  i
i5  i
i9 
i 2  1
i6 
i10 
i 3  i
i7 
i11 
Question 1
Question 2
Question 3
Question 4
Complex Numbers
Complicated?
Try it!
+
Solve
x  6 x  10  0
2
Graph it!
Can you solve it graphically?
What do you notice?
Solve Algebraically!
x  6 x  10  0
2
Practice!
Simplify.
a)
4
b)
c)
8
d) 4  18
e)
 4   169
f)
 16
 10   15
Solve: