1.

Loucus of complex number satifyingare arg[(z-5+4i)//(z+3-2i)] = - pi//4 is the are of a circle

Answer»

whose radiusis `5sqrt(2)`
whose RADIUS is 5
whose length(of arc) is `(15pi)/(sqrt(2))`
whose centre is -2-5i

Solution :
`(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))`


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