- #1
dervast
- 133
- 1
Hi i am reading about signal and systems course . What i want to prove is not a problem that i have to solve is something that the books take for granted and i want to prove it so i ll be able at exams to reprove so i won't have to remember it, (if u don't believe me i can give u the course's pdf that states what i say. Btw i posted here cause i don't know where else i should post problems like that
I want to prove why
e^(-j*(theta))=cos(theta)-jsin(theta) (1)
i know that e^j(theta)=cos(theta)+jsin(theta) Why the minus sign affects the sin and not the cos
also i want to find out why cos(theta)=1/2[e^(j*theta)+e^(-j*theta)] (2)
My teachers book say that these things exist. It proves number (2) using Eulers equation.
I know that the angle theta can be found from theta=1/sin(y/(sqrt(x^2+y^2))
theta:is the angle of the complex number
z=x+jy
z=e*e^j(theta)
I have tried to solve the euler equation like that
e^j*theta=cos(theta)+j(sin(theta))
cos(theta)=e^j*theta-j(sin(theta))
I have tried to convert the j(sin(theta)) to something that has inside e^j*theta or something like that but i have failed :(
I am really very week converting exponential numbers to equations that include cosins and sins. If u have a good book for that that i can read it online please suggest it to me
Homework Statement
I want to prove why
e^(-j*(theta))=cos(theta)-jsin(theta) (1)
i know that e^j(theta)=cos(theta)+jsin(theta) Why the minus sign affects the sin and not the cos
also i want to find out why cos(theta)=1/2[e^(j*theta)+e^(-j*theta)] (2)
My teachers book say that these things exist. It proves number (2) using Eulers equation.
I know that the angle theta can be found from theta=1/sin(y/(sqrt(x^2+y^2))
theta:is the angle of the complex number
Homework Equations
z=x+jy
z=e*e^j(theta)
The Attempt at a Solution
I have tried to solve the euler equation like that
e^j*theta=cos(theta)+j(sin(theta))
cos(theta)=e^j*theta-j(sin(theta))
I have tried to convert the j(sin(theta)) to something that has inside e^j*theta or something like that but i have failed :(
I am really very week converting exponential numbers to equations that include cosins and sins. If u have a good book for that that i can read it online please suggest it to me