A) \[z=\frac{\sqrt{3}}{3}-i\]
B) \[z=\frac{\sqrt{3}}{3}+i\]
C) \[z=\frac{\sqrt{3}}{3}\pm i\]
D) None of these
Correct Answer: B
Solution :
\[2(x+iy)=\sqrt{{{x}^{2}}+{{y}^{2}}}+2i\] \[2x=\sqrt{{{x}^{2}}+{{y}^{2}}}\]and\[2y=2\]i.e. \[y=1\] \[4{{x}^{2}}={{x}^{2}}+1\]i.e., \[3{{x}^{2}}=1\]i.e., \[x=\pm \frac{1}{\sqrt{3}}\] \[x=\frac{1}{\sqrt{3}}(\because x\ge 0)\therefore z=\frac{1}{\sqrt{3}}+i=\frac{\sqrt{3}}{3}+i\]
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