Complex Numbers Flashcards
1
Q
(x1+iy1)+(x2+iy2)=
A
(x1+x2)+i(y1+y2)
2
Q
(x1+iy2)-(x2+iy2)=
A
(x1-x2)+i(y1-y2)
3
Q
(x1+iy1)(x2+iy2)=
A
(x1x2-y1y2)+i(x1y2+x2y1)
4
Q
z=x+iy
ż=
A
x-iy
5
Q
żz=|z|^2=
A
x^2 + y^2
6
Q
z1/z2=
A
(z1xż2)/(z2xż2)
7
Q
|z|=r=
A
sqrt(x^2 + y^2)
(Modulus/Absolute Value)
8
Q
When x>0 find arg(p)
A
tan(p)=y/x
9
Q
When x<0 find arg(p)
A
tan^-1(y/x) + pi = p
10
Q
Trigonometric/Polar form
z=
A
r(cosp + isinp)
11
Q
De moivre formula
A
(cosp+isinp)^n = cos(np)+isin(np)
12
Q
Take z=cosp+isinp and w=cosa+isina
zw=
arg(zw)=
A
cos(p+a)+isin(p+a)
arg(z)+arg(w)
13
Q
Take z=cosp+isinp and W=R(cosa+isina)
zW=
A
R(cos(p+a)+isin(p+a))
14
Q
arg(z^n)=
A
narg(z)
15
Q
Z=R1(cosp+isinp) and W=R2(cosa+isina)
ZW=
|ZW|= |Z||W|=
arg(ZW)=
A
ZW=R1R2(cos(p+a)+isin(p+a))
=R1R2
arg(Z)+arg(W)
