unit 2 _act 2_ powers and roots _4º eso_

8/3/2019 Unit 2 _Act 2_ Powers and Roots _4 ESO_

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Unit 2: Powers and Roots. ACTI

IES Albayzn (Granada)

RE

suggested to the same ske

It is important to understa

sense of the word. This mi

being called fictitious.

If you think of a number lin

and the numbers to the left

One way to think of an ima

Questions

Who starts using the letter

Why was the situation of c

Do you understand the jok

Could you represent the fol

26, 2 5

ITIES 2 Mathematic

DING: Complex Numbers

It may seem strange to just invent ne

that is how mathematics evolves.

negative numbers were not an ac

mathematics until well into the thirte

fact, these numbers often were referre

numbers.

In the seventeenth century, Rene D

square roots of negative numbers ima

an unfortunate choice of words, and s

letter i to denote these numbers. Thespticism as negative numbers.

nd that these numbers are not imaginary i

sleading word is similar to the situation of n

e, then the numbers to the right of zero are

of zero are negative numbers.

ginary number is to visualize it as up or dow

Argand Diagram. Just as we can graph a re

number line, we can graph a complex

accomplished by using one number line for

complex number and one number line for the i

complex number. These two number

perpendicular to each other and pass throu

origins, as shown on the left image.

The result is called the complex plane or the A

Jean-Robert Argand (1768-1822), an accou

mathematician. Although he is given credit fo

of complex numbers, Caspar Wessel (1

conceived the idea before Argand.

ito denote imaginary numbers?

mplex numbers similar to negative numbers

? Whats its meaning?

llowing numbers on the complex plane?

, 35, 4,

4 ESO Option B

Page 1

w numbers, but

For instance,

cepted part of

nth century. In

to as fictitious

escartes called

inary numbers,

tarted using the

e numbers were

in the dictionary

gative numbers

ositive numbers

from zero.

l number on a real

number. This is

the real part of the

maginary part of the

lines are drawn

gh their respective

rgand diagram after

ntant and amateur

this representation

745-1818) actually

?

5


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Unit 2: Powers and Roots. ACTIVITIES 2 Mathematics 4 ESO Option B

IES Albayzn (Granada) Page 2

Activities

1) Match the term with its description:

Index Irrationalnumber

Non-negativereal number

Rationalexponent

Product ruleof exponents

Product ruleof radicals

Distributiveproperty

Radicand Quotient ruleof exponents

Like radicals

a)

b) c) Radicals that have the same radicand and index.

d)

e) The expression under a radical sign.f) The 3 in

is an example of this.

g) A real number that is greater than or equal to 0.

h)

i) A number that cannot be written as a fraction in which the numerator and

denominator are integers.

j) In,

is this.

2) Put and X in the box if the number is an element of the set at the top of

the column:

WholeNumbers

Integers RationalNumbers

IrrationalNumbers

RealNumbers

ComplexNumbers358

817

60.40

278 250.97 20

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Unit 2: Powers and Roots. ACTIVITIES 2 Mathematics 4 ESO Option B

IES Albayzn (Granada) Page 3

3) The formula for the volume of a cylinder is = ; where V is thevolume, r is the radius, and h is the height. Solve for r, this formula is

=

. If the volume of a circular swimming pool is 3052 ft3 and is

depth is 3 ft, find its radius ( = 3.14. Round to the nearest wholenumber. Convert the result into meters.4) Drug Potency. The amount A (in milligrams) of digoxin, a drug taken by

cardiac patients, remaining in the blood t hours after a patient takes a 2-

miligram dose is given by = 2 10 ..a) How much digoxin remains in the blood of a patient 4 hours after

taking a 2-miligram dose?

b) Suppose that a patient takes a 2-miligram dose of digoxin at 1:00

P.M. and another 2-miligram dose at 5:00 P.M. How much digoxin

remains in the patients blood at 6:00 P.M.

c) Suppose that a patient takes a 2-miligram dose of digoxin, when will

we be able to observe a 50% reduction of the dose taken in the

patients blood?

5) Simplify each radical and then combine like terms

a) =+ 188325

b) =+++ 33

633

992481

a

c) 232398 =d) =+ 3333 102125080

2

12703

6) Simplify each expression by rationalizing the denominator. Write the

result in simplest form.

a) =b) =c)

=d)

=e)

=f)

=g) =

unit 2 _act 2_ powers and roots _4º eso_

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