Radicals Packet Worksheet Page 4
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1
2
3
4
5
6Imaginary and Complex Numbers
Since the square root of a negative number is not real, a different type of number was invented
to represent them. Imaginary numbers come from taking the square root of a negative
number. The following is useful when dealing with imaginary numbers.
= − =
( )
i
1
i
= ⋅
= ⋅
=
5
4
i
i i
i
1
i
( )
2
=
−
= −
( )( )
2
= ⋅
= −
= −
i
1
1
6
2
4
i
i i
1 1
1
( )
( )( )
= ⋅
= ⋅ − = −
= ⋅
= −
= −
3
2
7
3
4
i
i i
i
1
i
i
i i
i
1
i
( )( )
( ) ( )
= ⋅
= −
− =
=
⋅
=
⋅
=
4
2
2
8
4
4
i
i i
1
1
1
i
i i
1
1
1
22
This pattern will always repeat and continue. When asked to simplify something like
i , just
divide 22 by 4. The remainder is 2. The reason this is done is that for every power that is a
2
multiple of 4, the result is one (see above examples). The next step is to evaluate
i . Here is
what is actually happening.
( )
( )
5
=
⋅
=
⋅
=
⋅
=
= −
5
22
20
2
4
2
2
2
i
i
i
i
i
1
i
i
1
( )
5
20
4
4
Using the power of a power rule, the term
i
can be rewritten as
i
. The term
i is used
i = .
4
inside the parenthesis because
1
Evaluate and simplify each of the following.
−
9 −
−
−
3
A)
B)
12
C)
27
D)
49
−
8 −
−
− −
3
E)
121
F)
G) 4
16
H)
54
−
−
2
17
254
I)
75
J)
3i
K)
12i
L)
6i
i −
218
417
2436
513
M)
16i
N)
i
O)
17i
P)
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