2. I

CompedNurnberg

2X = 6

.

x= i

VI = VI

X = I HT

• I . ← IT . Fs =3

l =L

If:÷÷:Tf

i"

-- i ?i =- i. i = - i' = - C- 1) = I

is = ii. i = I - i = i

it = - I Powers of i start repeatingI = - i

after the 4th power of i

- look for the remainder whenIf = I

*

dividing by 4

remaindersimplify

2040 Mutt. of 4

Is

. i i j20430=÷:*-

i. iti4e-

-- -

→TT✓

i -

- ITWe can express square roots

of negative radicand s using in.

exd

-

VIGVIOLHIT = IF VIVI HI ifI Gi

isrius d I

it -362456 =i 36 - 6 5ik2=5ri

=④i t t

Complex Numbers-

The set of all numbers in the form :

with a,

b EIR

→ a is the Real Part

→ bi is the Imaginary part→ if a- o the number is a pure imaginary

NumberZi

2 → a= 2 b -

- O

2 Gt ZiIR CE

a- 6 b=2

T- a-

Real numbers a= o b= - 7are a subset

of complex number

To

simplifywrite a complex number

in standard form ( at bi )*If b is a radical i may be

written Deford the constant

-3 t i v 's

Equality of complex numbers-

a. b.c.DE/Ratbi=Ctdi

If and only if

a- - C and b=d

operations with complex numbers

Addingandfubtraa.in#9bs9dElR(atbi)t(ctdi)=@tc)tbtd) i

⇐Catbi ) - ¢tdi ) -

- @-c) t ( b - d) i

(4-121)+(7+31)=(4+7)+(-12+31)i=Ht9i

(8t2i ) - GZ - si )-18

- to )t(2- C-D) i= 10+71

Multiplying-

Use distribution and FOIL as needed

asex

. Gi(5-91)=6 i. s - Gi . 9i-

T-

=3 Oi - 54 it=3 Oi - 54ft )

=

305+54=54+301

( - 4t2i ) ( G - ziguse FOIL

f4. 6)t f4 . ti ) t @i.6) t @i .

- Ii )F O

l L= -24 t 28 it 12 i t - 14 i

2 ←

= -24 tl4t28¥i=-I0t4