logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

$z=\large\frac{7-i}{3-4i}$ then $z^{14}$ equals

$\begin{array}{1 1}(A)\;2^7&(B)\;2^7i\\(C)\;-2^7i&(D)\;\text{None of these}\end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
$z=\large\frac{7-i}{3-4i}\times \frac{(3+4i)}{(3+4i)}=\frac{25+25i}{25}$
$\Rightarrow 1+i$
$\Rightarrow z=\sqrt 2(\cos \large\frac{\pi}{4}$$+i\sin\large\frac{\pi}{4})$
$\Rightarrow z^{14}=2^7(\cos \large\frac{14\pi}{4}$$+i\sin \large\frac{14\pi}{4})$
$\Rightarrow z^{14}=2^7(-i)$
$\Rightarrow -i2^7$
Hence (C) is the correct answer.
answered Apr 10, 2014 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...