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
weather prediction on monsoon past data on project

apllication in business and economics

The government is auctioning off oil leases at two sites. At each site, 100,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes and Alexis Pickens are bidding for the

We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f


Two circles touch each other externally: Given: Two circles with respective centres C1 and C2 touch each other externaly at the point P. T is any point on the common tangent

QR is the tangent to the circle whose centre is P. If QA ||  RP and AB is the diameter, prove that RB is a tangent to the circle.

Consider a database whose universe is a finite set of vertices V and whose unique relation .E is binary and encodes the edges of an undirected (resp., directed) graph G: (V, E). Ea

f(x)=4x-3 and g(x)=(x+3)/4 a)Find the function fg(x) b)Hence describe the relationship between the functions f and g c)Write down the exact value of fg(sqrt(3))