How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{11 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 11 pi)/8 i)$ using trigonometric functions?

Question

How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{11 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 11 pi)/8 i)$ using trigonometric functions?

1 Answer

Impact of this question

1318 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-19T06:51:15

$1.139 + 1.183 i$ $1.139+1.183i$

Explanation:

Euler's formula says that

$e^{i x} = cos x + i sin x$ $e^(ix)=cosx+isinx$ .

Using values from the question of $x = \frac{π}{12}$ $x=pi/12$ and $x = \frac{11 π}{8}$ $x=(11pi)/8$ ,

$e^{\frac{π}{12} i} = cos (\frac{π}{12}) + i sin (\frac{π}{12})$ $e^(pi/12i)=cos(pi/12)+isin(pi/12)$
$= cos 15 + i sin 15$ $=cos15+isin15$
$= 0.966 + 0.259 i$ $=0.966+0.259i$

$e^{\frac{11 π}{8} i} = cos (\frac{11 π}{8}) + i sin (\frac{11 π}{8})$ $e^((11pi)/8i)=cos((11pi)/8)+isin((11pi)/8)$
$= cos 247.5 + i sin 247.5$ $=cos247.5+isin247.5$
$= - 0.383 - 0.924 i$ $=-0.383-0.924i$

Substituting these values into the question,

$(0.966 + 0.259 i) - (- 0.383 - 0.924 i)$ $(0.966+0.259i)-(-0.383-0.924i)$
$= 0.966 + 0.383 + 0.259 i + 0.924 i$ $=0.966+0.383+0.259i+0.924i$
$= 1.349 + 1.183 i$ $=1.349+1.183i$

Science

Math

Humanities

... and beyond

How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{11 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 11 pi)/8 i)$ using trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you evaluate eπ12i−e11π8ie^( ( pi)/12 i) - e^( ( 11 pi)/8 i) using trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you evaluate $e^{\frac{π}{12} i} - e^{\frac{11 π}{8} i}$ $e^( ( pi)/12 i) - e^( ( 11 pi)/8 i)$ using trigonometric functions?