InterviewSolution
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InterviewSolution
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Let `z_1 and z_2` be two complex numbers satisfying `|z_1|=9` and `|z_2-3-4i|=4` Then the minimum value of `|z_1-Z_2|` isA. 1B. 2C. `sqrt(2)`D. 0 |
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Answer» Correct Answer - D Clearly `|z_1|=9 ` represents a circle having centre `C_1(0,0)` and radius `r_1=9` and `|z_2-3-4i|=4` represents a circle having centre `C_2(3,4)` and radius `r_2=4` The minimum value of f`|z_1-z_2| ` is equals to minimum distance between circless `|z_1|=9` and `|z_2-3-4i|=4` `therefore C_1 C_2= sqrt((3-0)^2(4-0)^2)= sqrt(25)=5` and `|r_1-r_2|=|9-4|=5 rArr C_1C_2 = |r_1-r_2|` `therefore `Circles touches each other internally . Hence , `|z_1-z_2|_(min)=0` |
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