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







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