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If z1,z2, are two complex number such that |z1|=|z2|=2 and |z1+z2| =square root 3 , then |z1-z2|equals

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Solution: $left | z_1+z_2 ight |^2+left | z_1-z_2 ight |^2=2left | z_1 ight |^2+2left | z_2 ight |^2$

$Rightarrow$ $3+left | z_1-z_2 ight |^2=2(2)+2(2)$

$Rightarrow$ $left | z_1-z_2 ight |^2=5Rightarrow left | z_1 -z_2 ight |=sqrt5$

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Deependra Verma

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