Download Day 3 - Creating Quadratic Equations, Complex

MHF 4UI
Unit 1 Day 3
Review of Prerequisite Skills
A. Creating Quadratic Equations
Warm up - Solve the following quadratic equation by factoring:
a2 – 4a – 21 = 0
Now, let’s try to write possible quadratic equations in the form ax2 + bx + c = 0 from the
given roots.
a) 3 and -
1
4
c) 2  5 and 2 - 5
b)
3 and - 3
d)
2- 3
2 3
and
5
5
MHF 4UI
Unit 1 Day 3
B. Complex Numbers
Imaginary numbers, Im, are the result of the square roots of negative numbers.
Examples:
 3,
 15
The difficulty comes in dealing with the negative in the square root, so let’s deal with
that separately.
Definition: i =
so,
 3  3  -1  3  1  3 i
7 7 7
Recall:
so,
and
-1
- 1  - 1  -1
i2 = -1
i has no decimal value and cannot be graphed on a real number line.
A complex number, C, is a number of the form a + bi, where a, b  R and i =
-1
Examples: 5 – 2i, 7 + 6i, -4 + 6 3 i
Note: All real numbers are complex numbers and can be written in the form a + bi.
5 = 5 + 0i
- a rational now written in complex form
2 3 = 2 3 + 0i - an irrational now written in complex form
Imaginary numbers can also be written in complex form a + bi.
4i = 0 + 4i
-7 3 i = 0 - 7 3 i
Updated number system tree diagram:
C =   Im
MHF 4UI
1. Simplify.
a)  9
Unit 1 Day 3
b)
c)
 16
 37
d)
 75
2. Evaluate.
a) (3i)(4i)
b) (5i)(-4i)
3. Simplify.
a) 5   24
b) 6 -  18
c) 4i(2 + 3i)
e) (6 + 3i)(5 + 2i)
f) (3 + 2i)(3 – 2i)
d) (5 + 2i)(3 – 4i)
g) (x – 4 + 3i)(x – 4 – 3i)
4. Simplify.
a)
10  - 32
2
b)
- 15  - 75
10
c)
18 - - 72
24
e)
 12