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


√-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
Discuss demanding total market demand verus gaing market share

The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number

Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers [7] 2.2 In a given day he will

A. Design an investigation that details the following six components:

a sail has a spread of canvas as measured 12'',12'', 15'' and 9'' and it has 90 degrees. Find the area of one side of the sail

assignment on theorems on circle for class 9

How many ways can six men and three women form a line if no two women may stand behind each other?


Example: Write down the equation of the line which passes through the two points (-2, 4) and (3, -5). Solution At first glance it might not appear which we'll be capable to

Price Cutter sold 85 beach towels for $6.95 each. What were the total sales? You must multiply the number of towels sold through the price of each towel; 85 × $6.95 = $590.75.