NIMCET 2019 Question Paper with solutions

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Question : 43 of 120

Marks: +1, -0

If |z| <

√3 - 1

, then |

\z^2

+ 2z cos α| is

less than 2
$√3 + 1$
$√3 - 1$
None of these

Solution:

Given

|z| < √3-1

|z^2+2z\cosα| ≤ |z^2|+|2z\cosα|

=|z^2|+2|z||\cosα|

≤ |z^2|+2|z|

< (√3-1)^2+2(√3-1)

< 3+1-2√3+2√3-2

< 2

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