Question

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

Answer 1

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))`