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