Algebra 2



Algebra 2 / Trig Name

Section 5.4 Complex Numbers Block Date

Review:

[pic]_______ because ____ * ____ = 4

[pic]_______ because ____ * ____ = 9

[pic]_______

Imaginary Numbers

Imaginary number = _______________ Symbol = ___________

Ex: [pic] Ex: [pic] Ex: [pic]

i = i2 =

Complex Numbers

Complex numbers = combine imaginary and real numbers Ex. 5 + 3i

Adding and Subtracting

Add the corresponding numbers and imaginary coefficients

Examples:

1. (3 + 4i) + (5 – 3i) = 2. (2+ 3i) – (4 – 2i) = 3. (2 – 4i) – (-2 + 3i) =

Practice:

4. (5 + 6i) + (4 – 2i) = 5. (3+ 8i) – (12 – 10i) = 6. (1 – 11i) – (-4 + 9i) =

Multiplication

****When multiplying it is important to remember the powers of i****

Examples:

1. 5i(-2 + i ) = 2. (7 – 4i) (-1 + 2i) = 3. (6 + 3i) (6 – 3i) =

Practice:

4. 6i(-10 + 3i) = 5. (11 – 2i) (-5 + 7i) = 6. (5 + 4i) (8 – 10i) =

Division

In order to divide you need to multiply the numerator or denominator by the conjugate of the denominator.

Examples:

1. [pic] 2. [pic]

Practice:

3. [pic] 4. [pic]

5. [pic] 6. [pic]

Homework: Page 277 #37, 39, 41, 47-60 First Column

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