logo

Ask Questions, Get Answers

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

No of complex numbers satisfying $\overline{z}=iz^2$ is

$\begin{array}{1 1}(A)\;1&(B)\;2\\(C)\;3&(D)\;4\end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
$\overline{z}=iz^2$
$\Rightarrow |\overline{z}|=|iz^2|$
$\Rightarrow |z|=|i||z^2|\Rightarrow |z|=0$ or $| z|=1$
$|z|=0\Rightarrow z=0$
$|z|=1\Rightarrow z\overline{z}=1$
Thus,$\overline{z}=iz^2$
$\Rightarrow \large\frac{1}{z}$$=iz^2\Rightarrow z^3=-i$ or $i^3$
$\Rightarrow (\large\frac{z}{i})^3$$=1\Rightarrow z=i,i\omega,i\omega^2$
Hence (D) 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
...