Download GUIDED NOTES – Lesson 2-5

GUIDED NOTES – Lesson 2-5
Complex Numbers
Name: ______________________ Period: ___
Objective: I can add, subtract, multiply, and divide with complex numbers.
Sometimes we will encounter equations that have no real solutions, so we have to rely on a number system with the
imaginary unit, indicated by the letter _____.
We can take the square root of positive numbers like
answer is _______.
9 equals _____ because _____ = 9, technically the correct
But when we try to take the square root of a negative number like  9 we can’t do it because no number multiplied
by itself will give you a negative. It has to be either (3)(3) = 9 or (-3)(-3) = 9.
IMAGINARY NUMBERS
i  1
i  1
2
EXAMPLES:
 121
 28
(5)( 2i )
(3i )( 2i )
A COMPLEX NUMBER is a combination of a _____________ number and an ________________ number.
You can add and subtract complex numbers in the same way you have combined algebraic expressions. Keep your real
terms and imaginary parts _____________________.
(-2 + 5i) + (1 – 7i)
(4 + 6i) – (-1 + 2i)
When you multiply complex numbers use the ______________ method that you are already familiar with. Then
combine like parts. However you must simplify further by replacing i2 with _____.
(2 + 4i)(9 – 3i)
(1 + 4i)(3 – 6i)
COMPLEX CONJUGATES - When dividing complex numbers, your final answer can’t have ____ in the denominator.
2+3𝑖
8
2+𝑖
𝑖
1+2𝑖
1−𝑖
SOLVING QUADRATIC EQUATIONS
5x2 + 20 = 0
3x2 + 5 = -67