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If w is a non real imaginary cube root of unity ,then find argument(iw)+arg(iw^2)

If w is a non real imaginary cube root of unity ,then find argument(iw)+arg(iw^2)

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Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
Dear Ved
Β 
arg(π‘–πœ”)+arg(π‘–πœ”2)=arg π‘’π‘–πœ‹/2.𝑒2π‘–πœ‹/3+arg π‘’π‘–πœ‹/2.𝑒4π‘–πœ‹/3
=arg 𝑒7π‘–πœ‹/6+arg 𝑒11π‘–πœ‹/6
=(7πœ‹/6βˆ’2πœ‹)+(11πœ‹/6βˆ’2πœ‹)
[as the argument should be in the principal range]
=3πœ‹βˆ’4πœ‹=βˆ’πœ‹
Β 
Regards
Arun(askIITians forum expert)

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