2 Complex/Imaginary Numbers WHAT IS?There is no real number whose square is -25 so we have to use an imaginary numberWHY?“i” is an imaginary number. “i” is equal to the square root of -1BASICALLY: any time you see a negative under a SQUARE ROOT an “i” gets pulled out.
3 Simplifying Radicals with Imaginary Numbers ALWAYS pull the “i” out first before multiplying together.
4 Adding & Subtracting Complex Numbers A complex number is a number with “i” in it.Complex numbers can be written in the form :Imaginary partReal partTo add or subtract complex numbers combine the real parts and combine the imaginary parts separately.
6 Multiplying Complex Numbers You multiply complex numbers like you would binomials. (Double Distribute, Box, FOIL…etc)
7 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 signCONJUGATE =CONJUGATE =CONJUGATE =
8 Rationalize the Denominator SimplifyImaginary # song
9 iSince “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 2What about higher exponents? 4-7?4 goes into 33, 8 times with a remainder of 1