Complex Numbers What are complex numbers and how are they simplified?

Slide 2:

Complex number: any number in the form a + bi where
i =
Add and Subtract:
1. (2 + 7i) + (3 – 5i) 2. (6 – 3i) - (7 – 2i) Treat “i” as you would any variable.
Remember: You can only add or subtract “like terms” 5 – 2i (6 – 3i) + (-7 + 2i) Since it’s subtraction,
Change the signs in the
Second quantity -1 - i

Slide 3:

Multiply:
(8 + 2i)(7 – 3i) 2. (8 – i)(3 + 2i)
3. (5 + 4i)(5 – 4i) FOIL just as you would if it were “x” 56 – 24i + 14i – 6i2 I2 = -1 56 – 24i + 14i – 6(-1)
56 – 24i + 14i + 6 Combine like terms 62 – 10i 24 + 16i – 3i – 2i2
24 + 16i – 3i – 2(-1)
24 + 16i – 3i + 2 26 + 13i 25 – 20i + 20i – 16i2
25 – 20i + 20i – 16(-1)
25 – 20i + 20i + 16
41 Note the set up of this problem –
The “imaginary” term canceled itself!

Slide 4:

“Divide” -
You cannot have a radical in the denominator and
“I” is a radical! You need to rationalize the
Denominator!
1. In order to “eliminate” the i in the denominator, multiply by i. This must
be done to the numerator also so we are only multiplying by 1! Since i2 = -1…

Slide 5:

Let’s look at another!

Slide 6:

That process doesn’t work for this type though. Instead,
Remember the problem where the “I” canceled out? We
Need to multiply by the “conjugate” The “conjugate” is 4 + 2i Distribute the numerator
FOIL the denominator I2 = -1 Simplify

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

Send to Blogs and Networks

Processing ....

Premium member

Use HTTPs

HTTPS (Hypertext Transfer Protocol Secure) is a protocol used by Web servers to transfer and display Web content securely. Most web browsers block content or generate a “mixed content” warning when users access web pages via HTTPS that contain embedded content loaded via HTTP. To prevent users from facing this, Use HTTPS option.

By: rahulprati (48 month(s) ago)

plz let me download it......