Locus of complex number satisfying arg[(z−5+4i)(z+3−2i)]=−π4 is the arc of a circle
A
whose radius is 5√2 units
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B
whose radius is 5 units
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C
whose length (of arc) is 15π√2 units
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D
whose centre is −2−5i
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Solution
The correct option is D whose centre is −2−5i
z0−(−3+2i)z0−(5−4i)=BDADeiπ/2=i ⇒z0+3−2i=iz0−5i−4 ⇒z0=−2−5i ⇒ Radius AD=|5−4i−(−2−5i)| =|7+i| =√50=5√2 units
Length of arc =34 (perimeter of circle) =34(2π×5√2) =15π√2 units