## Presentation on theme: "Unit 4Radicals Complex numbers."— Presentation transcript:

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.

ALWAYS pull the “i” out first before multiplying together.

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.

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