Imaginary & Complex Numbers
Obj: Simplify expressions with imaginary numbers; re-write radicals as complex expressions.
Why do imaginary numbers exists and how do you add/subtract/multiply/divide imaginary numbers?
What do we need imaginary numbers? Allows us to make calculations that
otherwise would not be possible (ex. Electric circuits)
= ____________ = __________
Square roots with a negative radicand should be re-written using the letter “i”
Calculator: To use the imaginary number press
2nd , ___
Simplify your answers to #4 - #5 using the calculator
1. 2.
3. 4.
Re-write each radical as using the value “i” a. b.
Re-write each radical as using the value “i” c. d.
#1 Simplify
#2 Simplify
COMPLEX NUMBERS
Real #sEx) 2, -5,
1.3
Imaginary #s
Ex) 5i
RationalIrrationalIntegers etc. a+bi
a) Simplify )31()46( ii
b) Simplify )73()64( ii
c) Simplify
d) Simplify
Conjugate
The opposite operation of two terms.
Ex) 5 + 2i conjugate: 5 – 2i
Imaginary numbers may never be in the denominator
To eliminate them, multiply the numerator & the denominator by the conjugate
a)
i
i
42
3
b)
c)