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  • Help me please, - Complex numbers and quadratic equations - JEE Main-3

Let \left |z-1-i \right |=2 and \left |z-4-5i \right |=3 are equations of two circles, then number of common solutions between them equals

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Answers (1)

best_answer

first circle has centre (1,1) & radius = 2

2nd circle has centre (4,5) & radius = 3

\therefore distance between cenytres = \therefore \sqrt{9+16}=r=5cm of radius 

so, circles will touch externally .

Equation of circle -

\left |z-z_{0} \right |=r 

z_{0} = centre of circle

r= radius of circle

z lies on circle.

- wherein

Locus of z will be a circle as z is always at a fixed distance r from a fixed point z_{0}

z=x+iy,  z_{0}=x_{0}+iy_{0}

 

 


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