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)