Complex Numbers Flashcards
1
Q
Argument of a complex number
A
For z= a+bi
tan(theta)=b/a
2
Q
coshx in exponential form
A
1/2(e^x+e^-x)
3
Q
sinhx in exponential form
A
1/2(e^x-e^-x)
4
Q
de moivres theorum
A
cosnx + isinnx = (cosx+isinx)^n
5
Q
lnz
A
ln(magnitude of z) + i theta
6
Q
cosh^2x-sinh^2x=
A
1
7
Q
sinh(A±B)=
A
sinhAcoshB±coshAsinhB
8
Q
cosh(A±B)=
A
coshAcoshB ±sinhAsinhB
9
Q
sin(A±B)
A
sinAcosB±cosAsinB
10
Q
cos(A±B)
A
cosAcosB∓sinAsinB
11
Q
1-tanh^2z
A
sech^2z
12
Q
coth^2z-1
A
cosech^2z
13
Q
arcsinhx=
A
ln[x+sqrt(x^2+1)]
14
Q
arccoshx=
A
ln[x+sqrt(x^2-1)]
