CHAPTER I
ALGEBRA
IMAGINARY NUMB .
, Complex numbers
im
Mod Arg form
^
f.
-
ztzi
-
Atgument
Malthus
.
stars . Re
length angle , a
✓
In the cartesian plane :
rcosoy
x
=
rsino =
In the complex plane
'
. .
:
iy softy
x +
Z
where
=
r -
Z =
rasa + irsing
a =
ardan E)
* check which side of plane
|zP=zE=
'
( xtiy ) ( iy ) x2ty
K twhehicmhoisudus
- =
.
, Multiplication in
Moaargformb "
it
"
.
apparently makes easier .
z
=
r ( case + isina )
W
=
s ( cos 0 + isino )
zw =
rs ( case + is in a) ( casa + is in 0 )
=
rs ( cosacosol -
sin Asin0 + icososih 0 + isinoeas ¢ )
*
compound angle formula
=
rs
[ Cosca + 0 ) + is in late ) ]
{ *(
/*
meds add angles
multiply
Example : its + i ) =
-1 -
irz
iirtii
;t¥I
.IE?ItEKiEilma:yjF iff
.
"
=
any
ALGEBRA
IMAGINARY NUMB .
, Complex numbers
im
Mod Arg form
^
f.
-
ztzi
-
Atgument
Malthus
.
stars . Re
length angle , a
✓
In the cartesian plane :
rcosoy
x
=
rsino =
In the complex plane
'
. .
:
iy softy
x +
Z
where
=
r -
Z =
rasa + irsing
a =
ardan E)
* check which side of plane
|zP=zE=
'
( xtiy ) ( iy ) x2ty
K twhehicmhoisudus
- =
.
, Multiplication in
Moaargformb "
it
"
.
apparently makes easier .
z
=
r ( case + isina )
W
=
s ( cos 0 + isino )
zw =
rs ( case + is in a) ( casa + is in 0 )
=
rs ( cosacosol -
sin Asin0 + icososih 0 + isinoeas ¢ )
*
compound angle formula
=
rs
[ Cosca + 0 ) + is in late ) ]
{ *(
/*
meds add angles
multiply
Example : its + i ) =
-1 -
irz
iirtii
;t¥I
.IE?ItEKiEilma:yjF iff
.
"
=
any
