1. Unit 4Radicals
Complex numbers

2. 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.

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 part
Real part
To add or subtract complex numbers combine the real parts and combine the imaginary parts separately.

5. Adding & Subtracting Complex Numbers

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 sign
CONJUGATE =
CONJUGATE =
CONJUGATE =

8. Rationalize the Denominator
Simplify
Imaginary # song

9. 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