Trigonometry_ Ice Cream life: October 2012

Sunday, October 28, 2012

Imaginary numbers

Hi^.^
another math blog for YOU ALL !!!

Today's question is : How do we operate on imaginary numbers?

So... to get started what are imaginary numbers?

A imaginary number is i , it represents all imaginary numbers.

For example when we have a negative square root and we say that there isn't a "real world solution" we say that because you cant square a negative number.

To make those negative square roots have a real answer we use a special number called the: imaginary number represented as = i or
√-1

For example :

√-9 = √-1 √9

we use the value of i which equals √-1 and then multiply it

by the positive square root 9. we then square root the 9.

And get:

√-9= 3i

lets say you have a more complicated expression like: i3 Then we have to know the more complicated process of i

i=i

i2=-1
if we already that i2 =-1
we can then figure out that 13 equals -i because we can multiply the -1*i and get -1

Following this cycle we can say that i4 equals 1 because
(-1)(-1) = 1.
(-1)(-1) are used because their exponents i2*i2 give i4

for i5 we multiply (-i)(-1) and it gives us +i

the cycle:
i= i
i2=-1
i3= -i
i4 = 1
i5= +i

Now you try :D

√-25

√-100

i360

i4926

GOODBYE AND REMEMBER :D

works cited:
Just for you:http://worshipsounds.files.wordpress.com/2012/03/just-for-you.gif
Heart math: http://mentalfloss.cachefly.net/wp-content/uploads/2008/11/math_tee2.jpg

Sunday, October 21, 2012

The weird FIRST time

MY FIRST POST(yay!^.^)

Hello, everyone :D

this is the second blog about math D;

(Yea,yea) we all hate math like typical teenagers, but I have to do it because of my teacher :(

but enough of introductions

its the dreading time (tan,tan,tan)

Trigonometry Time

Question:

"Why do we flip the inequality symbol when multiplying by a negative number or solving absolute value inequalities?"

okay, so here we go ^.^ on our foot journey:)...

For example, if we had a statement like: 20 > 12 then it would be true, but lets say that that you are told to multiply both numbers by a negative number ?

what do we do now ?? :O

have no fear I will explain :)

In my example,we will multiply each side by -2.

20(-2) < 12(-2)

your outcome will be:

-40 > -24 and this is false because -40 is lesser than -24

To make it clear I made a number line ---->

In a number line, the positive numbers show amount of value by having the numbers closer to zero value less while the numbers father away from zero have a greater value.

But for the left side of the number line if the numbers are closer to zero then their amount of value higher than the numbers father away from zero.

therefore if -42 is more farther from zero then it has a lesser value than -24 since it is much more closer.

Back to our problem, if : -42 > -24

it would be incorrect because like we said before -42 has a lower value than -24 because it is the more farther away than -24.

DO YOU GET IT NOW?

So, we change the sign to number one : have the correct sign when dealing with negative numbers

In absolute inequalities you change the sign for the same reason

for example :

I2x+1I >6

you would first make two separate equations

like:

2x+1>6 and 2x+1<-6.

2x+1>6 :

In this case we are saying that 2x+1 is greater than 6

2x+1<-6

In this equation we switched the sign and made the 6 negative, because from the previous equation we only had the answer of a full set of positive numbers not the negative numbers .