Question

Separate the real and imaginary parts from the following complex number: cos(a+ib)

Also, what is the Magnitude and phase of the above complex number?

Answer 1

I think you can use
cos(x+y)= cos(x) cos(y) - sin(x) sin(y)

and
cos(ix)= cosh(x)
sin(ix)= i sinh(x)

Answer 2

Thats interesting! I should have supplied the hint now that I think about it. The hint that came with this problem is cos(X) = 1/2[e^(iX)+e^-(iX)].

I think I have all the answers besides phase, so if I could just get help for phase I would appreciate that!

Answer 3

I think I have all the answers
in that case, what did you get for the real and imag parts ?

Answer 4

For real I got: [(0.5e^-b)*cos(a)+(0.5e^b)*cos(a)]
For imaginary: [(0.5e^-b)*isin(a)-(0.5e^b)*isin(a)]

Answer 5

I think you use
for x+iy
mag = sqrt( x^2 + y^2)
phase = atan( y/x)

It looks ugly for your expressions.

Answer 6

Do you agree that I have the correct real/imaginary parts? I know, it looks real ugly huh lol

Answer 7

yes, they look good.

you could use the definition of cosh(b)= (e^b + e^-b)/2
and sinh(a) = (e^a - e^-a)/2 to write them as
cos(a)cosh(b) - i sin(a) sinh(b)
if you know about cosh and sinh

Answer 8

Yes I think I can do that. Thank you very much phi!