A) \[-\frac{3}{5}-\frac{1}{5}i\]
B) \[-\frac{1}{5}+\frac{3}{5}i\]
C) \[-\frac{1}{5}-\frac{3}{5}i\]
D) \[\frac{1}{5}-\frac{3}{5}i\]
Correct Answer: C
Solution :
Given \[a>0\] \[z=\frac{{{\left( 1+i \right)}^{2}}}{a-i}=\frac{2i\left( a+i \right)}{{{a}^{2}}+1}\] Also\[|z|=\sqrt{\frac{2}{5}}\Rightarrow \frac{2}{\sqrt{{{a}^{2}}+1}}=\sqrt{\frac{2}{5}}\Rightarrow a=3\] So\[\overline{z}=\frac{-2i(3-i)}{10}=\frac{-1-3i}{5}\]You need to login to perform this action.
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