Power of iota, Mathematics

The next topic that we desire to discuss here is powers of i. Let's just take a look at what occurring while we start looking at many powers of i.

i1 = i                                                    i1 = i

i2  = -1                                               i2  = -1

i3  =i ⋅ i2  = -i                                        i3  = -i

i4  = (i2 )2  = ( -1)2  = 1                         i4 = 1

i5 = i ⋅ i4  = i                                          i5  = i

i6 = i2 ⋅ i4  = ( -1) (1) = -1                    i6  =-1

i7 = i ⋅ i6  = -i                                        i7  = -i

i8  = (i4 )2  = (1)2  = 1                            i8  = 1

Can you notice the pattern?  All powers if i can be reduced down to one of four probable answers and they repeat every four powers continuously. It can be a convenient fact to remember.

Next we need to address an issue on dealing along with square roots of -ve numbers.  we know that we can do the following.

1075_Power of iota.png

In other terms, we can break up products within a square root into a product of square roots provided both numbers are positive.

It turns out that actually we can do the same thing if one of the numbers is -ve.  For instance,

523_Power of iota1.png

However, if both of numbers are negative it won't work anymore as the following shows.

371_Power of iota2.png

We can summarize it as a set of rules.  If a & b are both positive numbers then,

2238_Power of iota3.png

Consider the following example to know it's important.

Posted Date: 4/6/2013 3:28:12 AM | Location : United States







Related Discussions:- Power of iota, Assignment Help, Ask Question on Power of iota, Get Answer, Expert's Help, Power of iota Discussions

Write discussion on Power of iota
Your posts are moderated
Related Questions
A farmer has a rectangular field of length 100m and breadth 70m. He leaves a path of 1m all along the boundary inside it. He decides to apply a manure to the remaining part of the

Determination of the Regression Equation The determination of the regression equation such given above is generally done by using a technique termed as "the method of least sq

Probability -Probability is an extremely popular concept in business management. Since it covers the risks such may be included in certain business situations. This is a fact

1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.

Mike, Dan, Ed, and Sy played together on a baseball team. Mike's batting average was 0.349, Dan's was 0.2, Ed's was 0.35, and Sy's was 0.299. Who had the highest batting average?

Kelly plans to fence in her yard. The Fabulous Fence Company charges $3.25 per foot of fencing and $15.75 an hour for labor. If Kelly requires 350 feet of fencing and the installer

1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.

A man sold an item for Rs 6,750 at a loss 25%. What will be the selling price of same item if he sells it at a profit of 15%?

A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??

Find the  least  number that  is  divisible by all  numbers between 1  and  10  (both inclusive). Ans: The required number is the LCM of 1,2,3,4,5,6,7,8,9,10 ∴ LCM = 2  × 2