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Grade: 11

                        

i want solution of question number 21. Please also give me a easy trick for solving this question in jee if exists.

5 months ago

Answers : (1)

Vikas TU
12276 Points
							
Dear student 
Given : | z₁ | = | z₂ | = | z₃ | = 1 ............. (1) 
. . . . . . | 1/z₁ + 1/z₂ + 1/z₃ | = 1 ............ (2) 
__________________________ 
To Find : | z₁ + z₂ + z₃ |. 
__________________________ 
We note that 
(i) | z | = | z' |, ... z' is conjugate of z 
(ii) z·z' = | z |² = | z' |² 
(iii) Σ(z') = [ Σ(z) ]'. 
__________________________ 
If | z | = 1, then : z·z' = 1, i.e., (1/z) = z'...... (3) 
∴ | z₁ + z₂ + z₃ | 
= | ( z₁ + z₂ + z₃ )' | 
= | (z₁)' + (z₂)' + (z₃)' | 
= | 1/z₁ + 1/z₂ + 1/z₃ | ........ from (3) 
= 1 ...................................... from (2) 
__________________ 
∴ | z₁ + z₂ + z₃ | = 1 
 
5 months ago
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