CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Complex Numbers

Simplify : ...

Question

Simplify : $\frac{{(sin π / 8 + i cos π / 8)}^{8}}{{(sin π / 8 - i cos π / 8)}^{8}}$

Open in App

Solution

${(\frac{sin π / 8 + i cos π / 8}{sin π / 8 - i cos π / 8})}^{8}$

$= (\frac{sin π / 8 + i cos π / 8}{sin π / 8 - i cos π / 8} \times \frac{sin π / 8 + i cos π / 8}{sin π / 8 + i cos π / 8})$

$= {⎛ ⎜ ⎜ ⎝ \frac{sin π / 8 + i cos π / 8}{{sin}^{2} \frac{π}{8} + {cos}^{2} \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8}$

$= {(sin \frac{π}{8} + i cos \frac{π}{8})}^{16}$

$= {[cos (\frac{π}{2} - \frac{π}{8}) + i sin (\frac{π}{2} - \frac{π}{8})]}^{16}$

$= {(cos \frac{3 π}{8} + i sin \frac{3 π}{8})}^{16}$
$= cos \frac{3 π}{2} + i sin \frac{3 π}{2}$

$= 0 - i$

$= - i$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The value of

(s i n \frac{π}{8} + i cos \frac{π}{8})^{8} (s i n \frac{π}{8} - i c o s \frac{π}{8})^{8}

{⎛ ⎜ ⎜ ⎝ \frac{sin \frac{π}{8} + i cos \frac{π}{8}}{sin \frac{π}{8} - i cos \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8}

Q. Show that one value of

{⎛ ⎜ ⎜ ⎝ \frac{1 + sin \frac{π}{8} + i cos \frac{π}{8}}{1 + sin \frac{π}{8} - i cos \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{\frac{8}{3}}

- 1

Q. The value of

{(sin \frac{π}{8} + i cos \frac{π}{8})}^{8}

Q. The expression

{⎡ ⎢ ⎢ ⎣ \frac{1 + sin \frac{π}{8} + i cos \frac{π}{8}}{1 + sin \frac{π}{8} - i cos \frac{π}{8}} ⎤ ⎥ ⎥ ⎦}^{8} =

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Complex Numbers

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon