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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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5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

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