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 (\varpit)

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!