+132 
To simplify this expression, we can factor out the common denominator of 60:
[e^(17pi*i)/60] + [e^(57pi*i)/60] = (e^(17pi*i) + e^(57pi*i)) / 60
Now, we can use Euler's formula to write each exponential term in terms of sines and cosines:
e^(17pi*i) = cos(17pi) + i*sin(17pi) = -1 + 0i = -1
e^(57pi*i) = cos(57pi) + i*sin(57pi) = -1 + 0i = -1
Substituting these values into the expression, we get:
(e^(17pi*i) + e^(57pi*i)) / 60 = (-1 - 1) / 60 = -1/30
Therefore, the simplified expression is -1/30.
e^(17*pi*i/60) + e^(57*pi*i/60)
= 0.629 + 0.777i - 0.987 + 156i
= -0.358 + 0.933i
+397 Use the trig identities
\(\displaystyle \cos(A)+\cos(B)=2\cos\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right) \\ \text{and} \\ \displaystyle \sin(A)+\sin(B)=2\sin\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right).\)
The common
\(\displaystyle \cos\left(\frac{A-B}{2}\right)\)
term will be equal to \(\cos(\pi/3)=1/2,\)
cancelling out the 2's.
