Expressing a complex number as an Exponent

[elsamp123]

Homework Statement

Express as z = Re[Ae^(i($\varpi$ t+ $\alpha$)]
1. z = cos($\varpi$ t - $\pi$/3) - cos ($\varpi$t)

2. z= 2sin($\varpi$ t) + 3 cos ($\varpi$ t)

3. sin($\varpi$ t ) - 2 cos ($\varpi$ t - $\pi$/4) + cos ($\varpi$ t)

Homework Equations

I used cos A + cos B; A = (a²+b²)^(1/2); and tan($\theta$) = y/x

The Attempt at a Solution

I read the other doubt regarding nearly the same questions, and as much as i tried to figure it out, i couldn't understand how to separate the parts and arrive at the same answer as the textbook requires. Could you please show me in a few more steps. thank u

 

[issacnewton]

use euler's formula. http://en.wikipedia.org/wiki/Euler's_formula

so $$\cos(x)=Re(e^{ix})\;\;\sin(x)=Im(e^{ix})$$

 

[elsamp123]

Thanks a ton.. Sorry for the late reply, i finally was able to figure it out whew!