1. ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)@
SECTION 4-8 : COMPLEX NUMBERS

2. Solve the equation that corresponds to your group number.
x2 = -100
m2 = -200
z = -8
11 – 5r2 = -49
100s = 400
5p2 – 12 = p2 – 13
-3(n + 5)2 = 9

3. We all know :

4. Find :
Now, let’s re-visit those equations.

5. An imaginary number has an “i” in it.
Complex Number : is in Standard Form, a + bi , where a and b are real numbers.
Pure Imaginary numbers have a = 0.
Complex Conjugate : The complex conjugate of a + bi is a – bi.
Find the complex conjugate of each number.
13) 7 + 5i
14) 6 – 7i
15) i
16) -3 - i
17) 14i
18) 24

6. Graph each Complex Number. Use an Argand Diagram.
Imaginary
Axis
15) -4 – 3i
16) 3 – 4i
17) i
18) 5i
Real
Axis

7. Given z1 = 3 + 4i, z2 = 5 – 2i, and z3 = 10 + i, find
22) z1 + z2
23) z2 – z3
29)
24)
5 • z3
30)
25) i • z2
31)
26) z1 • z2
27) z3 • z2

8. i0 = 1
i4 = i2 • i2 = -1 • -1 = 1
i1 = i
i5 = i4 • i = 1 • i = i
i2 = -1
i6 = i5 • i = i • i = i2 = -1
i3 = i2 • i = -1 • i = -i
i7 = i6 • i = -1 • i = -i
MEMORIZE this chart : i0 = 1
i1 = i
i2 = -1
i3 = -i

9. Simplify.
32) i237
33) i1492
34) i2018
35) i795
36) i
Remember : The divisibility test for 4 – the last two digits of a number must be divisible by 4 for the number to be divisible by 4.
37) i

10. ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)
Solve in your groups.
x2 + 2x – 24 = 0
6x2 + 19x + 10 = 0
x2 – 8x + 25 = 0
x2 – 4x – 1 = 0

11. Now humor me and do the following…
ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)
Take your answers, add them
together and then take the
opposite of your answer.
Take your answers and multiply them together.
Do you notice anything special????

12. ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)
So……….. Standard Form : ax2 + bx + c = 0 if s1 and s2 are the solutions of a quadratic equation, then

13. Find the quadratic equation with the following solutions
ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)
Find the quadratic equation with the following solutions
38) 8 and -11

14. Like….a really important theorem……
Irrational and imaginary zeros for quadratic equations (really, any equations) must come in conjugate pairs.

15. ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)
Find the quadratic equation with real-number coefficients if one or more solutions is (are) …

16. ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)
Factor.
My math teacher told me you can’t factor these.
43) x2 + 25
44) 64x2 + 49
45) 4x2 + 9
46) -9x2 - 25