logo

Ask Questions, Get Answers

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

If $z$ is a complex number so that $iz^2-\overline z=0$, then $|z|= ?$

$\begin{array}{1 1}(A) \;0 \;or \;1 \\(B)\;0 \;or\; \large\frac{\sqrt 3}{2} \\(C)\;1\;or \;\large\frac{\sqrt 3}{2} \\(D)\; 0 \;or\;\large\frac{1}{20} \end{array}$

Can you answer this question?
 
 

1 Answer

0 votes
Let $z=x+iy$
$z^2=x^2-y^2+2xyi$
$\overline z=x-iy$
$iz^2-\overline z=0$
$\Rightarrow\:i(x^2-y^2+2xyi)-(x-yi)=0$
$\Rightarrow\:(x^2-y^2+y)i-(2xy+x)=0$
$\Rightarrow\:x^2-y^2+y=0\:and\:2xy+x=0$
$\Rightarrow\:x=0\:or\:y=\large-\frac{1}{2}$
If $x=0,\:then\:-y^2+y=0$
$\Rightarrow\:y=0\:\:or\:\:1$
If $y=\large-\frac{1}{2}$, then $x^2-\large\frac{1}{4}$$-\large\frac{1}{2}$
$\Rightarrow\:x=\pm\large\frac{\sqrt 3}{2}$
$\therefore\:z=(0,0),\:or\:(0,1),\:or\:(\large\frac{\sqrt 3}{2},-\frac{1}{2}$), $(\large-\frac{\sqrt 3}{2},-\frac{1}{2}$)
$\Rightarrow\:|z|=0\:or\:1$
answered Jul 17, 2013 by rvidyagovindarajan_1
edited Jul 17, 2013 by rvidyagovindarajan_1
 

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
...