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COMPLEX NUMBERS Unit 4Radicals

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Complex/Imaginary Numbers WHAT IS? WHY? There is no real number whose square is -25 so we have to use an imaginary number 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 : Real part Imaginary 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 dont 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 =

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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. What about higher exponents? 4-7? 4 goes into 12, 3 times with a remainder of zero. 4 goes into 22, 5 times with a remainder of 2 4 goes into 33, 8 times with a remainder of 1

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