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If z1,z2,z3 are complex numbers such that |z1| =|z2|=|z3| =|1/z1 +1/z2 +1/z3 |=1 then |z1+z2+z3| is

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Solution:

$left | z_1 ight |=left | z_2 ight |=left | z_3 ight |=1$

$Rightarrow$ $z_1arz_1=z_2arz_2=z_3arz_3=1$

$herefore$ $left | z_1+z_2+z_3 ight |=left | 1/arz_1+1/arz_2+1/arz_3 ight |=left | 1/z_1+1/z_2+1/z_3 ight |=1$

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Deependra Verma

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