2Complex/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.
3Simplifying Radicals with Imaginary Numbers ALWAYS pull the “i” out first before multiplying together.
4Adding & 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.
6Multiplying Complex Numbers You multiply complex numbers like you would binomials. (Double Distribute, Box, FOIL…etc)
7Dividing 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 =
8Rationalize the Denominator SimplifyImaginary # song
9iSince “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