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  • Solve this problem - Let be two complex numbers satisfying and Then the minimum value of is : - Complex numbers and quadratic equations - JEE Main

Let z_{1}\: \: and\: \: z_{2}  be two complex numbers satisfying \left | z_{1} \right |=9  and  \left | z_{2}-3-4i \right |= 4. Then the minimum value of \left | z_{1}-z_{2} \right |  is :  

  • Option 1)

    2

     

  • Option 2)

    \sqrt{2}

  • Option 3)

    1

  • Option 4)

    0

Answers (1)

best_answer

 

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}

 

 


Option 1)

2

 

Option 2)

\sqrt{2}

Option 3)

1

Option 4)

0
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