Complex numbers, Mathematics

Complex Numbers

In the radicals section we noted that we won't get a real number out of a square root of a negative number.  For example √-9 isn't a real number as there is no real number which we can square & get -ve  9.

We now also saw that if a and b were both positive then √(ab) = √a√b .For a second let's forget that limitation and do the following.

√-9 =498_Complex Numbers.png = √9 √ -1 = 3 √-1

 Now, √-1 is not a real number, however if you think about it we can do this for any square root of a negative number.  For example,

√-100 =√100√-1=10√-1

√-5=√5√-1

√-290=√290√-1 etc.

Thus, even if the number isn't a perfect square still we can always reduce the square root of a -ve number down to the square root of a +ve number (which we or a calculator can deal with) times √-1 .

Thus, if we only had a way to deal with √-1 we could really deal with square roots of negative numbers.  Well the reality is that, at this level, there only isn't any way to deal with

√-1. Thus rather than dealing with it we will "make it go away" so to speak using the following definition.

                                               i =√-1

Note that if we square both of sides of this we get,

                                             i2  = -1

It will be significant to remember this later on. It shows that, in some way, i is the only "number" which we can square and acquire a negative value.

By using this definition all the square roots above become,

√-9 = 3i                              √-100=10i

√-5=√5i                              √-290 = √290 i

These all are examples of complex numbers.

Posted Date: 4/6/2013 3:16:07 AM | Location : United States







Related Discussions:- Complex numbers, Assignment Help, Ask Question on Complex numbers, Get Answer, Expert's Help, Complex numbers Discussions

Write discussion on Complex numbers
Your posts are moderated
Related Questions

Explain Multiplying/Dividing Negative Fractions? There are 3 steps to multiplying or dividing fractions. 1. If any negative signs are present, place them next to the numerator

how do you divide fractions?

One of the more significant ideas that we'll be discussing in this section is slope. The slope of a line is a measure of the steepness of any particular line and it can also be uti

i have trouble going through problem in this lesson. Markdown and Markups are theh ones im stuck in

Rate of Change : The first interpretation of derivative is rate of change.  It was not the primary problem which we looked at in the limit chapter, however it is the most signific


A cyclist, after riding a certain distance, stopped for half an hour to repair his bicycle, after which he completes the whole journey of 30km at half speed in 5 hours.  If the bre

Let E = xy + y't + x'yz' + xy'zt', find (a)   Prime implicants of E,  (b)  Minimal sum for E.  Ans:  K -map for following boolean expression is given as: Prime implic

Index Shift - Sequences and Series The main idea behind index shifts is to start a series at a dissimilar value for whatever the reason (and yes, there are legitimate reasons