Warm up: Questions

Answers 1)

2)

3 12 68a b

9 15x y

4 22a b

4 7x y xy

HW:Pg 253 #8-12, 19-26

Complex NumbersLesson 4.8

Square root of a negative real number Necessary Vocab

Imaginary unit: is the complex number whose square is -1.

So, and

i2 1i

1

2

3

4

1

1

1

MEMORIZE

i i

i

i i

i

1 1a a a i a : 5 5Ex i

1i

Vocabulary Imaginary number: any number of the form

where a and b are real numbers and a bi

a bi

0b

Imaginary PartReal

Part

More Vocabulary Complex number: can be written in the form

where a and b are real numbers.Ex: 3 + 5i

Pure imaginary number: can be written in the form , where a=0 and

Ex: 5i

a bi

0ba bi

1) Adding and Subtracting Complex Numbers What is the sum or Difference

4 3 5 7i i

4 5 3 7i i

2 4i

2) T.O.O. (Try On Own)

(7 2 ) ( 3 i)i

1 5 3 2i i

4 i

2 9i

3) Multiplying complex numbers

What is each product? 3 5 2i i

215 6i i

15 6 1i

6 15i

4) T.O.O: HINT* remember how you multiplied binomials in Algebra 1 (FOIL)

4 3 1 2i i

24 8 3 6i i i

4 8 3 6( 1)i i

2 11i

5) One more of multiplying complex numbers

6 6i i

236 6 6i i i

36 6 6 ( 1)i i

37

Remember difference of

Square Binomials?!?

6) Dividing Complex Numbers: lets do this together9 123i

i 3

3ii

2

2

27 369i ii

27 36 ( 1)9( 1)i i

36 279i

4 3i

7) A little more complex

2 31 4

ii

1 41 4

ii

2

2

2 8 3 121 4 4 16

i i ii i i

2 8 3 12( 1)1 4i 4i 16( 1)

i i

10 1117

i

10 1117 17

i

Now it is your turn

Questions Answers 8)

9)

5 23 4

ii

7 2625 25

i

46ii 1 2

6 3i

Mixed Review

Questions Answers

10)

11)

12)

3 9 3 9i i 18i

7 3i i 21

8 78 7

ii

15 112113 113

i

More math Jokes

Homework

Pg 253 #8-12, 19-26