QUIET complex-3
Algebra
Level
pending
if Z is a complex number satisfying the equation |Z+i| + |Z-i|=8 ,on the complex plane then the maximum value of |Z| is -
NOTE : |Z|= {(real part of Z)^2+(imaginary part of Z)^2}^1/2
6
8
2
4
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1 solution
|z+i| we can imagine as distsnce from point z in complex plane to point -i. As well |z-i| is distance from z to i. Ammount of distances point z from points -i, i (i.e.(0,-1) and (0,1) on y axis) is 8. So we are searching point z on ellipse with foci on y axis and semi major axis 4. Maximal modulus have points (0,4) and (0,-4) on major axis and its modulus is 4.