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If (a1+ib1)(a2+ib2)......(an+ibn)=A+iB, ...

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

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

B

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

C

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

D

none

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-COMPLEX NUMBERS -EXERCISE 1
  1. If the first term and common ratio of a G.P are both (1//2) (sqrt(3)+i...

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  2. sum(n=0)^oo((2i)/(3))^n=

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  3. If (a1+ib1)(a2+ib2)......(an+ibn)=A+iB, "then "Tan^(-1)(b1/a1)+Tan^(-1...

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  4. The real value of theta for which the expression (1 -isin theta)/(1 + ...

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  5. If (1-sintheta)/(1+2isintheta) is purely imaginary then theta=

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  6. If (3+2isintheta)/(3-2isintheta) is real , then theta =

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  7. A value of theta for which (2+3isintheta)/(1-2isintheta) is purely ima...

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  8. If (tanalpha-i[sin(alpha//2)+cos(alpha//2)])/(1+2isin(alpha//2)) is pu...

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  9. Find the general value of x if the expression (sin ""(x)/(2) + cos"" (...

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  10. The principal value of the argument -sqrt(3)+i is

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  11. The amplitude of 1+costheta+isintheta is

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  12. The amplitude of (1+sqrt(3)i)/(sqrt(3)+i) is

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  13. If pi//5 and pi//3 are the arguments of barz1 and z2 then the value of...

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  14. If pi//3 and pi//4 are the arguments of z1 and barz2 then the value of...

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  15. If 2pi//3 and pi//6 are the arguments of barz1 and z2 then value of ar...

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  16. z=1+isqrt(3)rArr|Arg z|+|Argbarz|=

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  17. If z1 and z2 are two non - zero complex numbers such that |z1+z2|=|z1|...

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  18. If z1 and z2 are two non - zero complex numbers such that |z1+z2|=|z1-...

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

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  20. Let z,w be complex number such that barz+ibarw=0 and arg zw =pi . Then...

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