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Presentation transcript:

Warm-Up 1. 2. 3. 4.

5-4 Complex Number

CA Standard SWBAT: Understand how real and complex numbers are related Add, subtract, multiply, and divide complex numbers

SOLVE 3x2 + 15 = 0 3x2 = -15 x2 = - 5 x = What do we do now?

What do we do now? Thus, i = Rene Descartes proposed a solution. He proposed that the solution to the equation x2 = -1 be represented by a number i where i is not a real number. Thus, i =

Pure Imaginary Numbers For any positive real number b, where i is the imaginary unit, and bi is called a pure imaginary number.

So let’s go back and solve 3x2 + 15 = 0 x2 = - 5 x =

Example 1: Simplify the expression 1. 2. 3.

Example 2: Your Turn 1. 2. 3.

Expansion If , what is i2 equal to?

Expansion

They repeat. So what is i10 ? How about i25? So does this help? Notice Anything? They repeat. So what is i10 ? How about i25? So does this help?

Example 3: Simplify 1. 2.

Example 4: Your Turn Simplify 1. 2. 3.

pg. 264 #22-33 Your Homework