IMAGINARY NUMBER
Howdy Class! It's now my turn to do a Blog. Now I will attempt to explain today's lesson in a easy to understand way.Remember Simplifying Radicals back in Grade 10?
Well here's a little refresher:
For Example, if you have √200:
√200
= √100√2
= 10√2
So, what do you do if the radical is negative?
Well here's an example
If you have √-72 you just simplify it like normal except you take out the negative one.
Here's what I mean:
√-72
= √36√2√-1
= 6√2√-1
HOW CAN THIS BE? THE SQUARE ROOT OF -1 IS NOT POSSIBLE!
Well... We're gonna pretend it is... and call it an IMAGINARY NUMBER represented by the letter i.
So what I'm saying is that i= √-1. So if i is the square root of -1, then i² must be -1.
Now how do you suppose to find i³? It goes something like this:
i³ = i² × i
= -1 × i
= -i
Remember Kids, when multiplying powers with the same base you ADD the exponents.
Now on to the next part: EQUATIONS WITH i
Ok, what if one day we're in class and then Ms. Ingram all of a all sudden throws this equation at us and says to put it into the simplest form in terms of i:
-5i(7i - 9)
WHAT DO YOU DO!? WHAT DO YOU DO!?
Don't worry... I will show you how to solve it.
STEP 1: MULTIPLY it out using distributive law.
So now your equation should look like this:
-35i²-45i
STEP 2: Substitute for the Values of i
-35(-1)+45i
=35+45i
That wasn't so hard but TRY THIS:
(3i² - 4)^4
I really hope you're not thinking about multiplying it out like this:
(3i² - 4)(3i² - 4)(3i² - 4)(3i² - 4)
That would just be simply WRONG!
This is how you really solve it:
(3i² - 4)^4
= (3(-1) - 4)^4
= (-3-4)^4
= (-7)^4
= -2401
There's one last thing I must show you folks and it is: RATIONALIZING EQUATIONS WITH i
Alright, here we go!
Sample Equation: 3i + 7
i - 2
STEP 1: Multiply the original fraction by the denominator with the sign switched over. For Example, if you have √3 + 3, you multiply it by √3 - 3. In this case, we will multiply it by i + 2.
3i + 7 (i + 2)
i - 2 (i + 2)
= 3i + 6i + 7i + 14
i² - 4
= 3i² + 13i + 14
i² - 4
= 3(-1) + 13i + 14
(-1) - 4
= -3 + 14 + 13i
- 5
= 11 + 13i
-5
That pretty much wraps up my post. Hope you guys understand it, especially you Justus because you couldn't be in class today. Well, hope your hand heals back.
Peace out
WAIT! I almost forgot. The next scribe shall be... Kristina.
posted by AnhThi @ 10:26 PM
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