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If (a(1) + ib(1)) (a(2) + ib(2)) … (a(n)...

If `(a_(1) + ib_(1)) (a_(2) + ib_(2)) … (a_(n) + ib_(n)) = A + iB` then
`Tan^(-1) ((b_(1))/(a_(1))) + Tan^(-1) ((b_(2))/(a_(2))) + …. + Tan^(-1) ((b_(n))/(a_(n))) = `

A

`Tan^(-1) ((A)/(B))`

B

tan^(-1) ((B)/(A))`

C

`Tan^(-1) ((2A)/(B))`

D

`npi + Tan^(-1) ((B)/(A))`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
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  2. Let z,w be complex number such that barz+ibarw=0 and arg zw =pi . Then...

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  3. If (a(1) + ib(1)) (a(2) + ib(2)) … (a(n) + ib(n)) = A + iB then Tan^...

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  4. If z and omega are two non-zero complex numbers such that |zomega| =1...

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  5. If z is a complex number of unit modulus and argument theta then, arg ...

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  6. sqrt(4ab - 2i (a^(2) - b^(2) ) =

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  7. x + isqrt(x^(4) + x^(2) + 1)) =

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  8. If sqrt(x+ iy) = pm (a + ib) then sqrt(x-iy) =

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  9. (1 - omega) (1 - omega^(2)) (1 - omega^(4)) (1 - omega^(5)) (1 - omega...

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  10. If omega is a imaginary cube root of unity , then 225 + (3 omega + 8 o...

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  11. (1 - omega + omega^(2)) ( 1 - omega^(2) + omega^(4)) ( 1- omega^(4) + ...

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  12. If omega is a complex cube root of unity , then (x + 1) ( x + omega) (...

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  13. If 1 , omega , omega^(2) are the cube roots of unity , then (x + y + z...

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  14. 4 + 5 ( - (1)/(2) + (isqrt3)/(2))^(334) + 3 ( - (1)/(2) + (isqrt3)/(2)...

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  15. If a = cos "" (4pi)/(3) + isin "" (4pi)/(3) then ((1 + a)/(2))^(3n) =

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  16. If omega is a cube root of unity , then |{:( 1 , omega , 2 omega^(2)...

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  17. If x^(2) + x + 1 =0 , then the value of (x + (1)/(x))^(2) + (x^(2) + ...

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  18. If 1 , omega , omega^(2) are the cube roots of unity , then the roots...

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  19. If omega is a complex cube root of unity , then the value of (a + b o...

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  20. If omega is a complex cube root unity then sin { (omega^(10) + omega^(...

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