slide1
Download
Skip this Video
Download Presentation
Before we do anything else, put your computers away

Loading in 2 Seconds...

play fullscreen
1 / 14

Before we do anything else, put your computers away - PowerPoint PPT Presentation


  • 68 Views
  • Uploaded on

Before we do anything else, put your computers away. Imaginary Numbers. A beginning…. Before today, you couldn’t do the square root of a negative number. Today, that will change.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Before we do anything else, put your computers away' - tahir


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Before we do anything else,

put your computers away

a beginning
A beginning…

Before today, you couldn’t do the square root of a negative number.

Today, that will change.

In the beginning, mathematicians saw no need for these numbers outside of the classroom, so they game them the name “imaginary numbers”

slide4
However, electronic and other scientific applications have come to use them frequently. Unfortunately, the name, “Imaginary Numbers” has remained.
foundation
Foundation

The basis of the imaginary numbers is the square root of -1.

It is given the letter i.

i = √-1

So √-25 = √25 x √-1 = 5i

basically
Basically,

Any time you see a negative under a square root, you pull its “i” out. You do this before you do anything else.

√-36 x √-9 = 6i x 3i = 18i2

which leads to another problem
Which leads to another problem…

What in the world are we going to do with i2?

If i = √-1, then i2 = -1.

Also, i3 = -i

and i4 = 1.

adding and subtracting
Adding and Subtracting

(3 + 4i ) + (-2 + 6i ) = (3 + -2) + ( 4i + 6i)

= 1 + 10i

Just add the “real” parts and add the “imaginary” parts separately.

slide9
(-5 + 2i ) – ( 2 – 6i ) = (-5 + 2i ) + ( -2 + 6i )

When you’re subtracting, change the subtraction to addition by changing all the signs following the subtraction…just like we did before with parentheses!! Then combine like terms.

= -7 + 8i

multiplying
Multiplying

3i x 4i = 12i2 (remember that i2 = -1)

= -12 Isn’t that easy?

4i ( -3 + 2i ) Just distribute!!

-12i + 8i2 (remember that i2 = -1)

= -12i -8 and we usually write the real number first so we would put -8 – 12i

more multiplying
More Multiplying!!!

(-2 – 5i) (4 + 3i ) Just FOIL!!!

-8 – 6i – 20i – 15i2 (remember that i2 = -1)

-8 – 6i – 20i + 15combine like terms

= 7 – 26i isn’t that easy?

just one more multiplying
Just one more multiplying

(3 – 5i)2 = (3 – 5i) (3 – 5i)

= 9 -15i – 15i + 25i2

= 9 -15i – 15i – 25

= -16 – 30i

well maybe one more
Well…maybe one more

Do you remember how multiplying conjugates got rid of the radicals?

The same thing works here. Multiplying conjugates gets rid of i.

( -3 + 2i ) ( -3 – 2i ) = 9 + 6i – 6i – 4i2

= 9 + 6i – 6i + 4

= 13

now its up to you
Now its up to you

Your assignment is

5-9    pg 314    20, 22-24, 26-28, 31-33, 38- 42, 44-46, 48, 49

ad