A) 5
B) 10
C) 15
D) 20
Correct Answer: B
Solution :
As, z lies on the curve \[\arg (z+i)\,=\frac{\pi }{4},\] which is a ray originating from (-i) and lying right side of imaginary axis making an angle \[\frac{\pi }{4}\] with the real axis anticlockwise sense. \[\therefore \] The value of \[|z-(-4+3i)\,|\,\,+\,\,|\,\,z-(4-3i)\,|\] will minimum when \[z,-4+3i,\text{ }4-3i\]are collinear. \[\therefore \] Minimum value = distance between \[(-4+3i)\] and and \[\left( 4-3i \right)\] \[=\sqrt{{{(-4-4)}^{2}}\,+{{(3+3)}^{2}}}\,=\sqrt{64\,+36}\,=\sqrt{100}=10\]You need to login to perform this action.
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