# Complex Numbers by lindseypsenter

VIEWS: 1,383 PAGES: 18

• pg 1
```									Complex Numbers
Definition of pure
imaginary numbers:

Any positive real number b,
2        2
b  b  1  bi
where i is the imaginary unit
and bi is called the pure
imaginary number.
Definition of pure
imaginary numbers:

i  1
2
i  1
i is not a variable
it is a symbol for a specific
number
Simplify each expression.

1. 81        81 1  9i

2. 121x         121x 1 x
5         4

 11 i x
2
x
3. 200  100 1 2x
x
 10i 2x
Simplify each expression.
4. 8i  3i  24i  24  1
2
2
Remember i  1      24

5. 5 20  i 5 i 20
Remember that 1  i

 i  100 110  10
2
2
Remember i  1
i
Cycle of ""

i 1
0
i 1
4

i i
1
i i
5

i  1
2
i  1
6

i  i
3
i  i
7
Simplify.
12    To figure out where we
i        are in the cycle divide the
exponent by 4 and look at
the remainder.
12  4 = 3 with remainder 0
So i  i  1
12       0
Simplify.
17    Divide the exponent by 4
i        and look at the remainder.

17  4 = 4 with remainder 1

So i      17
i  i
1
Simplify.
26    Divide the exponent by 4
i        and look at the remainder.

26 4 = 6 with remainder 2

So i     26
 i  1
2
Simplify.
11    Divide the exponent by 4
i        and look at the remainder.

11 4 = 2 with remainder 3

So i  i  i
11      3
Definition of Complex
Numbers
Any number in form
a+bi, where a and b are
real numbers and i is
imaginary unit.
Definition of Equal
Complex Numbers
Two complex numbers are
equal if their real parts are
equal and their imaginary
parts are equal.
If a + bi = c + di,
then a = c and b = d
complex numbers, combine like
terms.
Ex: 8  3i  2  5i 
8  2  3i  5i

10  2i
Simplify.
8 7i 12 11i
8 12 7i  11i
4  18i
Simplify.
9 6i 12 2i 
9 12 6i  2i 
3  8i
Multiplying
complex numbers.
To multiply complex
numbers, you use the
same procedure as
multiplying polynomials.
Simplify.
8 5i2 3i
F    O    I     L
16 24i 10i 15i   2

16 14i  15
31 14i
Simplify.
6 2i 5 3i 
F   O     I     L
3018i  10i  6i   2

30  28i  6
24  28i

```
To top