IIT JEE , AIEEE Forum - Mathematics , Algebra

neeraj_agarwal_1990

greatest and the least values of |z₁+z₂| if z₁=24+7i and |z₂|=6 are

[ans: 31,19]

greatest value can be found out easily by triangle inequality....how to find min.?

rooney

24 + 7i is a point in 1st quadrant at distance 25.

|Z|=6 is a circle with center as origin with radius 6.

So, draw both the point and circle on a graph.

Max value of Z1+Z2 will be when we consider a point on the circle in 3rd quadrant along the line joining the center and Z1. Clearly, from graph it is visible that Z1-Z2 attains a max vlue of radius of circle + distance of Z1 from origin which is 31. Z1-Z2 is nothing but the line segment starting from Z2 and ending at Z1

Similarly consider another point in 1st quadrant. In this case length of Z1Z2 segment will be least (distance of Z1 from origin - Radius of circle) = 25-6 = 19

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