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  • Let z1 and z2 be two complex numbers satisfying |z1|=9 and |z2 -3-4i| Then the minimum value of |z1 -z2| is :

Let z1 and z2 be two complex numbers satisfying |z1|=9 and |z2 -3-4i| Then the minimum value of |z1 -z2| is :

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Solution: We have , left | z_1 ight |=9  and  left | z_2 -3-4i ight |=4

                 ecause         left | z_1pm z_2 ight |geqslant left | left | z_1 ight |-left | z_2 ight | ight |

                Rightarrow          left | z_2-(3+4i) ight |geq left | left | z_2 ight | -left | 3+4i ight | ight |

                                 left | z_2-(3+4i) ight |geq left | left | z_2 ight | -5 ight |

                Rightarrow                   4geq left | left | z_2 ight |-5 ight |Rightarrow left | z_2 ight |leq 9

                Hence ,          left | z_1 - z_2 ight |geq left | left | z_1 ight |-left | z_2 ight | ight |

              Rightarrow                     left | z_1-z_2 ight |geq left | 9-9 ight |     Minimum value will be 0.

         

Posted by

Deependra Verma

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