Imaginary & Complex Numbers EQ : Why do imaginary numbers exists and how do you...

Imaginary & Complex Numbers

EQ: Why do imaginary numbers exists and how do you add/subtract/multiply/divide imaginary numbers?

Why do we need imaginary numbers? Allow us to make calculations that

otherwise would not be possible (ex. Electric circuits)

i2=

 Powers of i i1 i2 i3 i4 i5 i6 i7 i7 ...

 Simplified form

i -1 -i 1 i -1 -i 1 ...

How to re-write radicals using “i”

Re-write as multiple of -1

Separate radicals

Substitute

Ex 1) Re-write using the number “i”

Ex 2) Simplify

Change to “i” form first!!!

Multiply

Substitute i2 = -1

Factor

Multiply coefficients

You Try! – Simplify each imaginary expression

a.

b.

c.

COMPLEX NUMBERS

Real #sEx) 2, -5,

1.3

Imaginary #s

Ex) 5i

RationalIrrationalIntegers etc. a+bi

Ex 3) Simplify )31()46( ii

Ex 4)

Ex 5)

Conjugate

The opposite operation between 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

Ex 6) Simplify by rationalizing the denominator

Multiply top & bottom by conjugate

Substitute i2 = -1

Ex 7) Simplify by rationalizing the denominator

Calculator: To use the imaginary number press

2nd ,

Exit Ticket: Use the calculator to simplify:

1.

2.

)31()46( ii

Homework

Homework

Homework

Homework

Homework

Homework