Defining complex numbers and (1.3.1)

September 15th, 2015

i i2

Definitions

Imaginary Unit : is the representation the non-real number .

Imaginary Number: Has the form , where and .

Complex Numbers: The combination of the real number system and the imaginary number system. Complex numbers are of the form , where is the real part and is the imaginary part.

ii−1

bi i = −1b≠0

a +bi abi

So if , then what is the value of ? Of ? Of ? Of ?

i = −1 i2 i3

i4 i5

And what about or ?i17 i52

Ex. 1: Identify the real and imaginary parts of the complex number . How do you know which is real

and which is imaginary?

1

2+

23i

Ex. 2: Rewrite each radical in simplest terms within the complex number system. (You should use the imaginary unit i when necessary.)

a)

b)

c)

d)

e)

−16

49

18

−48

−24

How do we determine whether or not we need to use for any radical?i = −1

Ex. 3: Rewrite each complex number as a radical (do not include the imaginary unit i).

a)

b)

c)

d)

e)

4i

9i

2i 3

3 7

6i 2

So what is the relationship between complex numbers, real terms, and imaginary terms.