Dividing Square Roots of Negative NumbersDivide.
(a)
Quotient ruleDivide.= 5
= 225
=
B
75
3
=
i 275
i 23
2 - 75
2 - 3
EXAMPLE 3
476 CHAPTER 8 Roots, Radicals, and Root Functions
NOW TRY
EXERCISE 3
Divide.
(a) (b)
2 - 48
23
2 - 72
2 - 8
CAUTION Using the product rule for radicals beforeusing the definition of
gives a wronganswer. Example 2(a)shows that
Correctbut Incorrect
so 2 - 4 # 2 - 9 Z 2 - 41 - 92.
2 - 41 - 92 = 236 = 6 ,
2 - 4 # 2 - 9 = - 6 ,
-b
(b)
Quotient ruleDivide.= 2 i NOW TRY
=i 24
=i
B
32
8
= 2 - 32 =i 232
i 232
28
2 - 32
28
OBJECTIVE 2 Recognize subsets of the complex numbers.A new set of
numbers, the complex numbers,are defined as follows.
First write all
square roots in
terms of i.Complex
numbers
a + bi,
a and b real Real
numbers
a + bi,
b = 0 Rational
numbersIrrational
numbersNon-
integersIntegersNonreal
complex
numbers
a + bi,
b = 0FIGURE 11*Some texts define bias the imaginary part of the complex number a+bi.Complex NumberIf aand bare real numbers, then any number of the form is called a
complex number.In the complex number the number ais called the real
partand bis called the imaginary part.*
a+bi,
abi
For a complex number if then which is a real number.
Thus, the set of real numbers is a subset of the set of complex numbers.If and
the complex number is a pure imaginary number.For example, 3iis a pure
imaginary number. A number such as is a nonreal complex number.A com-
plex number written in the form is in standard form.
The relationships among the various sets of numbers are shown in FIGURE 11.
a+bi
7 + 2 i
bZ 0,
a= 0
a+bi, b= 0, a+bi=a,
NOW TRY ANSWERS
- (a) 3 (b) 4 i