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The minimum distance of z_{1}=3+4i from \left |z-1-i \right |=2  equals 

  • Option 1)

    \sqrt{11}-2

  • Option 2)

    \sqrt{13}-2

  • Option 3)

    \sqrt{15}-2

  • Option 4)

    \sqrt{17}-2

 

Answers (1)

best_answer

As we learnt in

Equation of circle -

\left |z-z_{0} \right |=r 

z_{0} = centre of circle

r= radius of circle

z lies on circle.

- wherein

Locus of z will be a circle as z is always at a fixed distance r from a fixed point z_{0}

z=x+iy,  z_{0}=x_{0}+iy_{0}

 

\left | Z-1-i \right |=2  is a circle with centre (1,1) and radius 2.

Distance of Z1 from centre =\left | 3+4i-1-i \right |=\left | 2+3i \right |=\sqrt{13}

which is greater than radius of circle so Z1 lies outside circle so minimum distance of  Z1 from circle =\sqrt{13}-2

 

 


Option 1)

\sqrt{11}-2

This is incorrect

Option 2)

\sqrt{13}-2

This is correct

Option 3)

\sqrt{15}-2

This is incorrect

Option 4)

\sqrt{17}-2

This is incorrect

Posted by

Himanshu

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