2.2 Complex NumbersFri Feb 20

Do Now1) 2x^2 -8 = 0

2) (sinx)^2 – 2sinx + 1 = 0

Quiz Review

• Retakes by Thursday

The number i

• The number i is defined such that

and

Ex

• Express each number in terms of I• 1)

• 2)

• 3)

Complex Numbers

• A complex number is a number of the form a + bi, where a and b are real numbers.

• The number a is said to be the real part and the number b is said to be the imaginary part

Addition and Subtraction

• When adding and subtracting complex numbers, combine the real parts together and the imaginary parts together

Ex

• Simplify the following expressions• 1) (8 + 6i) + (3 + 2i)

• 2) (4 + 5i) – (6 – 3i)

Multiplication

• Complex numbers follow the same multiplication rules

• Remember: i^2 = -1

Ex

• Simplify each of the following• 1)

• 2)

• 3)

Powers of i

• Let’s look at the first 8 powers of I

• Notice how the same 4 values cycle!

Ex

• Simplify each of the following• 1) i^37

• 2) i^58

• 3) i^75

• 4) i^80

Conjugates and Division

• The conjugate of a complex number a + bi is a – bi

• These are considered complex conjugates

• Use complex conjugates to simplify rational expressions involving complex numbers

Ex

• Divide 2 – 5i by 1 – 6i

Closure

• Simplify i^24

• HW: p.198 #1-9 odds, 11-73 EOO, 75-83 odds