A) 2
B) 3
C) 6
D) 5
Correct Answer: D
Solution :
| \[{{z}^{3}}+\frac{3\,{{(\bar{z})}^{2}}}{|z|}=0\] |
| Let \[z=r{{e}^{i\,\theta }}\] |
| \[\Rightarrow \] \[{{r}^{3}}{{e}^{i\,3\theta }}+3\,r\,{{e}^{-\,i\,2\,\theta }}=0\] |
| Since 'r' cannot be zero |
| \[\Rightarrow \] \[r{{e}^{i\,5\theta }}=-\,3\] which will hold for |
| \[r=3\] and 5 distinct values of \['\theta '\] |
| Thus there are five solution. |
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