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Warm-Up

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5-4 Complex Number

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**CA Standard SWBAT: Understand how real and complex numbers are related**

Add, subtract, multiply, and divide complex numbers

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

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**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 =

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**Pure Imaginary Numbers**

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

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**So let’s go back and solve**

3x = 0 x2 = - 5 x =

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

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Example 2: Your Turn 1. 2. 3.

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Expansion If , what is i2 equal to?

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Expansion

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**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?

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Example 3: Simplify 1. 2.

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Example 4: Your Turn Simplify

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pg. 264 #22-33 Your Homework

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