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

The revenue and cost functions for producing and selling quantity x for a certain production facility are given below. R(x) = 16x - x 2 C(x) = 20 + 4x a)  Determine the p

Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,

NULL/ VOID/ EMPTY SET A set which has no element is known as the null set or empty set and is indicated by f (phi). The number of elements of a set A is indicated as n (A) and

If ABC is an obtuse angled triangle, obtuse angled at B and if AD⊥CB Prove that AC 2 =AB 2 + BC 2 +2BCxBD Ans:    AC 2 = AD 2 + CD 2 = AD 2 + (BC + BD) 2 = A


Give the Introduction to Scientific Notation? In mathematics, it can be very difficult and time-consuming to do calculations involving very large and very small numbers. This i

jamal works every morning in his garden. yesterday he worked 3 AND 3-4HOURS. HE SPENT 1-3 OF THE TIME PULLING WEEDS. HOW MANY HOURS DID JAMAL SPEND PULLING WEEDS?

how to make 2.3 into a fraction?

What do we mean by the roots of a quadratic equation ?