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5.4 Complex Numbers (p. 272)

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Imaginary Unit Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can! The imaginary unit is ¡. ¡= It is used to write the square root of a negative number.

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**Property of the square root of negative numbers**

If r is a positive real number, then Examples:

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***For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead.**

Example:

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Examples

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**Complex Numbers A complex number has a real part & an imaginary part.**

Standard form is: Real part Imaginary part Example: 5+4i

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The Complex plane Real Axis Imaginary Axis

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**Graphing in the complex plane**

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**Adding and Subtracting (add or subtract the real parts, then add or subtract the imaginary parts)**

Ex: Ex: Ex:

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**Multiplying Treat the i’s like variables, then change any that are not to the first power**

Ex: Ex:

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**Absolute Value of a Complex Number**

The distance the complex number is from the origin on the complex plane. If you have a complex number the absolute value can be found using:

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Examples 1. 2. Which of these 2 complex numbers is closest to the origin? -2+5i

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Assignment

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You can't take the square root of a negative number, right? When we were young and still in Algebra I, no numbers that, when multiplied.

You can't take the square root of a negative number, right? When we were young and still in Algebra I, no numbers that, when multiplied.

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