Unit 4Radicals Complex numbers

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.

Simplifying Radicals with Imaginary Numbers ALWAYS pull the “i” out first before multiplying together.

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.

Adding & Subtracting Complex Numbers

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

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 =

Rationalize the Denominator Simplify Imaginary # song

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