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