Locus of complex number satisfying `"a r g"[(z-5+4i)//(z+3-2i)]=pi//4` is the arc of a circle whose radius is `5sqrt(2)` whose radius is 5 whose length (of arc) is `(15pi)/(sqrt(2))` whose centre is `-2-5i`

Options

A. whose radius is `5sqrt(2)`
B. whose radius is 5
C. whose length (of arc) is `(15pi)/(sqrt(2))`
D. whose centre is -2-5i

Answer

A, B, C

Explanation

`(z_(0) - (-3+2i))/(z_(0)-(5-4i))= (BD)/(AD)e^(ipi//2)=i`
`rArr z_(0) +3-2i =iz_(0) - 5i -4`
`rArr z_(0) = - 2-5i`
`rArr " Radius" AD = |5-4i-(-2-5i)|`
`= |7+i|`
`= sqrt(50) = 5sqrt(2)`
Length of arc `= (3)/(4)` (Perimeter of circle)
`=(3)/(4)(2pixx5sqrt(2))`
`= (15)/(sqrt(2))`