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SHORT ANSWER TYPE QUESTIONSIfz - x + iy and P represents z in the Argand plane, find the locus of P when1)12 2-31

Answer»

given equation is|z-2-3i|=5 where z=x+iy

So |x-2+i(y-3)|=5

(x-2)^2+(y-3)^2=25

x^2+y^2-4x-6y-12=0 is the locus

let z=x+iy|(x+iy)-2-3i|=5|x+iy-2-3i|=5| (x-2) + i(y-3) |=5√[ (x+2)^2 + (y-3)^2 ] = 5squaring both the sides(x+2)^2 + (y-3)^2 = 5^2the equation is in the form of--(x+a)^2 + (y+b)^2 =(r)^2where r is the radius of circlewith centre(-a,-b)

Hence locus of the equation |z -2 -3i| = 5 is circle with radius r=5 and centre (-a,-b)=(-2,+3)


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