Need help with EE homework

[JohnCU]

x(t) = 7cos(100(pi)(t) - 3pi/4) + 5cos(100(pi)(t) + pi/2)

Find a complex-valued signal z(t) = Xe^(jw0t) such that x(t) = Re{z(t)}. Simplify z(t) as much as possible, so that you can identify its complex amplitude. Give the numerical values of X and w0.

So I did this...

z(t) = 7e^(-j(3pi/4)) + 5e^(j(pi/2))

7e^(-j(3pi/4)) = 7cos(-3pi/4) + j7sin(-3pi/4)

= -4.95 - j4.95

5e^(j(pi/2)) = 5cos(pi/2) + j5sin(pi/2)

= 0 + j5

-4.95 - j4.95 + j5 = -4.95 + j.05 right?

So z(t) = -4.95 + j.05

z(t) = 4.95e^(-j(pi/8))

Is that correct?

 

[Yossarian]

looks about right 😕 😕 😕 😕 😕 😕 😕 😕

 

[RaynorWolfcastle]

I read the question and I would solve it for you if I weren't so lazy. Unless you want to finish my Digital System Design lab for me 😛. If you want to know how to do it, just get rid of the 100Pi since they're irrelevant (multiples of 2Pi), then multiply and add. Unless you forgot a 'j' somewhere in your equation, both values are real so your angle is 0 and your magnitude is just adding the two numbers together.