Presentation on theme: "COMPLEX NUMBERS Unit 4Radicals. Complex/Imaginary Numbers WHAT IS? WHY? There is no real number whose square is -25 so we have to use an imaginary number."— Presentation transcript:
COMPLEX NUMBERS Unit 4Radicals
Complex/Imaginary Numbers WHAT IS? WHY? There is no real number whose square is -25 so we have to use an imaginary number 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 : Real part Imaginary 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 dont 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 =
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. What about higher exponents? 4-7? 4 goes into 12, 3 times with a remainder of zero. 4 goes into 22, 5 times with a remainder of 2 4 goes into 33, 8 times with a remainder of 1