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Unit 4Radicals Complex numbers

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**Complex/Imaginary Numbers**

WHAT IS? There is no real number whose square is -25 so we have to use an imaginary number WHY? “i” is an imaginary number. “i” is equal to the square root of -1 BASICALLY: any time you see a negative under a SQUARE ROOT an “i” gets pulled out.

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**Simplifying Radicals with Imaginary Numbers**

ALWAYS pull the “i” out first before multiplying together.

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**Adding & Subtracting Complex Numbers**

A complex number is a number with “i” in it. Complex numbers can be written in the form : Imaginary part Real part To add or subtract complex numbers combine the real parts and combine the imaginary parts separately.

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**Adding & Subtracting Complex Numbers**

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**Multiplying Complex Numbers**

You multiply complex numbers like you would binomials. (Double Distribute, Box, FOIL…etc)

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**Dividing Complex Numbers**

Remember that we don’t want to leave a radical in the denominator. To simplify a quotient, multiply by the conjugate of the denominator. Conjugate – change only the middle sign CONJUGATE = CONJUGATE = CONJUGATE =

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**Rationalize the Denominator**

Simplify Imaginary # song

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i Since “i” raised to a power follows a pattern you can easily find the answer by dividing the exponent by 4 and using the remainder to simplify. 4 goes into 12, 3 times with a remainder of zero. 4 goes into 22, 5 times with a remainder of 2 What about higher exponents? 4-7? 4 goes into 33, 8 times with a remainder of 1

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Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers.

Complex Numbers Add and Subtract complex numbers Multiply and divide complex numbers.

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