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
miaty and yesenia have a group of base ten blocks.Misty has six more than yesnia. Yesenia''s blocks repersent 17 together they have 22 blocks,and the total of blocks repersent 85.

Two people on bikes are at a distance of  350 meters.  Person A begin riding north at a rate of 5 m/sec and 7 minutes later on Person B begin riding south at 3 m/sec.  Determine th


how long is the radius of car tyre?


Product and Quotient Rule : Firstly let's see why we have to be careful with products & quotients.  Assume that we have the two functions f ( x ) = x 3   and g ( x ) = x 6 .

Determine or find out the domain of the subsequent function. r → (t) = {cos t, ln (4- t) , √(t+1)} Solution The first component is described for all t's. The second com

It is the full blown case where we consider every final possible force which can act on the system. The differential equation in this case, Mu'' + γu'  + ku = F( t) The displ

Allan has been hired to mow the school soccer field that is 180 ft wide through 330 ft long. If his mower mows strips which are 2 feet huge, how many times must he mow across the w

Caterer verifies that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If