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Complex Numbers question

2013 · Shift 1 · Q23

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2013 · Shift 1 · Q23

Complex Numbers question

2013 · Shift 1 · Q23

JEE AdvancedMathematicsComplex NumbersMCQ+4 / −1

Let complex numbers

\alpha \,and\,{1 \over {\overline \alpha }}\,

lie on circles

{\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2} = {r^2}

and

\,{\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2} = 4{r^2}

respextively. If

{z_0} = {x_0} + i{y_0}

satisfies the equation

2{\left| {{z_0}} \right|^2}\, = {r^2} + 2,\,then\,\left| a \right| =

A
${1 \over {\sqrt 2 }}$
B
${1 \over 2}\,$
C
${1 \over {\sqrt 7 }}$
D
${1 \over 3}$

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