Numbers!FROM
Complex SCRATCH (1.1) 10/10/2022
=- 1 Ex1.1 x 2x + 2 0 Ex1-2 2 2 + 2i
Towriteinmedsingshere
=
=
=
=
i F 22 2x
-
+1 10
+
=
121 5 252
= =
(n 1) -
-
=
1 1z1 is the modulus Im
2 - 1 i
=
argument
arg(z) is the
sir
arcan()
+H
x 1 In
=
↳
in
-
T
If the complexnumber I in the
lies
left side of the axes, you and to t i
z* is the
conjugate
complex Ex1.5 Repeated Multiplication and -
I
respectively
zx
cy
1zI(cos(arg(z)
=
+
*
z
x-in
=
Multiplication by : causes a rotation isin
+
larg(z1))
by I.
Ex1.6
Multiplying by z*
multiplying by conjugate a causes
something
similar to
rationalising in surds,
leftwith only real numbers. (n+iy)(n-iy) ni+y2
=
=Iz12
12110122
zz* 1z1 =
-ercluswz"ut?
zi (x iy)(n iy)
siye
=
+ -
=n"-y+ zxy:
zt ib roots!
Think about
sinncusy+ansusing a
simply
=
w a
=
+ -
w a 2-b2+labi
=
exponential form!
complex (1.2) Euler's formula can use -P, hella
waffl
iD
ein_cos cosP-isink
-
+ isine e =
Greig
-
phasor isjust
A a sinusoidal wave as a time-dependentfunction.
u(H Acos (wt 3)
=
+
FM?
remember on
from
Also:
x(H Acos(nt+2) + iAsin(nt + E)
=
cosO-
well sink= eio_eio
-
Just
functions!
hyperbolic like
Complex SCRATCH (1.1) 10/10/2022
=- 1 Ex1.1 x 2x + 2 0 Ex1-2 2 2 + 2i
Towriteinmedsingshere
=
=
=
=
i F 22 2x
-
+1 10
+
=
121 5 252
= =
(n 1) -
-
=
1 1z1 is the modulus Im
2 - 1 i
=
argument
arg(z) is the
sir
arcan()
+H
x 1 In
=
↳
in
-
T
If the complexnumber I in the
lies
left side of the axes, you and to t i
z* is the
conjugate
complex Ex1.5 Repeated Multiplication and -
I
respectively
zx
cy
1zI(cos(arg(z)
=
+
*
z
x-in
=
Multiplication by : causes a rotation isin
+
larg(z1))
by I.
Ex1.6
Multiplying by z*
multiplying by conjugate a causes
something
similar to
rationalising in surds,
leftwith only real numbers. (n+iy)(n-iy) ni+y2
=
=Iz12
12110122
zz* 1z1 =
-ercluswz"ut?
zi (x iy)(n iy)
siye
=
+ -
=n"-y+ zxy:
zt ib roots!
Think about
sinncusy+ansusing a
simply
=
w a
=
+ -
w a 2-b2+labi
=
exponential form!
complex (1.2) Euler's formula can use -P, hella
waffl
iD
ein_cos cosP-isink
-
+ isine e =
Greig
-
phasor isjust
A a sinusoidal wave as a time-dependentfunction.
u(H Acos (wt 3)
=
+
FM?
remember on
from
Also:
x(H Acos(nt+2) + iAsin(nt + E)
=
cosO-
well sink= eio_eio
-
Just
functions!
hyperbolic like
