How do you evaluate # e^( ( 11 pi)/6 i) - e^( ( 15 pi)/8 i)# using trigonometric functions?

1 Answer
Douglas K.
Mar 30, 2017

The general equation is:

#r_1e^(theta_1i) - r_2e^(theta_1i) = r_1cos(theta_1)-r_2cos(theta_2) + i(r_1sin(theta_1)-r_2sin(theta_2))#

Explanation:

You can derive the general equation, using Euler's Formula

#e^(thetai) = cos(theta) + isin(theta)#

#re^(thetai) = rcos(theta) + i(rsin(theta))#

For the given expression:

#e^((11pi)/6i) - e^((15pi)/8i) = cos((11pi)/6) - cos((15pi)/8) + i(sin((11pi)/6) - sin((15pi)/8))#

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