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JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1
If z1,z2,z3{z_1},{z_2},{z_3} be three complex numbers such that ∣z1+1βˆ£β‰€1,∣z2+2βˆ£β‰€2β€…β€Šandβ€…β€Šβˆ£z3+4βˆ£β‰€4\left| {{z_1} + 1} \right| \le 1,\left| {{z_2} + 2} \right| \le 2\;\mathrm{and}\;\left| {{z_3} + 4} \right| \le 4 then the maximum value of ∣z1∣+∣z2∣+∣z3∣\left| {{z_1}} \right| + \left| {{z_2}} \right| + \left| {{z_3}} \right| is
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Correct option: D
14
Option D (14) is correct because it represents the maximum possible value of the sum of the magnitudes of the complex numbers, which occurs when each complex number lies on the circle's circumference farthest from the origin.

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