| Direction (Q. Nos. 85) The geometrical meaning of \[|{{z}_{1}}-{{z}_{2}}|,\] where \[{{z}_{1}}\] and \[{{z}_{2}}\] are points in Argand plane is the distance between the points \[{{z}_{1}}\] and \[{{z}_{2}}\] based on this information, a class of problems about least value can be solved. The property that the sum of two sides of a triangle is greater than the third side is also very useful in solving these problems. |
A) \[\sqrt{2}\]
B) \[\sqrt{5}\]
C) \[2+\sqrt{13}\]
D) \[1+\sqrt{5}\]
Correct Answer: B
Solution :
\[|z-2+2i|+|\,z-3|\,\ge \,|z-2+2i-z+3|\] \[=|1+2i|\,=\sqrt{5}\] \[(\because \,\,|{{z}_{1}}|+|{{z}_{2}}|\,\ge \,|{{z}_{1}}-{{z}_{2}}|)\]
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