Question

How do you evaluate `e^( ( pi)/4 i) - e^( ( 7 pi)/6 i)` using trigonometric functions?

Answer 1

Pl use Euler's formula to evalute

Explanation:

Euler's formula is `e^(ix) = cosx+isinx`
So `e^(pi/4i)`-`e^(7pi/6i)`
`= cos(pi/4)+isin(pi/4) - ( cos(7pi/6)+isin(7pi/6))`
`= cos(pi/4)-cos(7pi/6)) +i ( sin(pi/4-sin(7pi/6))`
`= cos(pi/4)-cos(pi+pi/6)) +i ( sin(pi/4-sin(pi+pi/6))`
`= cos(pi/4)+cos(pi/6)) +i ( sin(pi/4+sin(pi/6))`
`= 1/sqrt2+sqrt3/2+i(1/sqrt2+1/2)`

please check it and give feed back