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If the complex number ` z_(1) " and " z_(2)` are such that `arg (z_(1)) - arg(z_(2)) = 0 ` and ` [|z_(1)| gt | z_(2)|]` , then show that ` |z_(1) - z_(2) | = | z_(1)| - |z_(2)| ` .

A

`|z_(1)|+|z_(2)|`

B

`|z_(1)|-|z_(2)|`

C

`||z_(1)|-|z_(2)|`

D

0

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The correct Answer is:
c
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
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  4. The join of z(1)=a+ib and z(2)=1/(-a+ib) passes through

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  5. If z(1),z(2),z(3),z(4) are the affixes of the four points in the Ar...

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  6. The value of sum(r=1)^(8)(sin((2rpi)/9)+icos((2rpi)/9)), is

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  7. If z(1),z(2),z(3),…,z(n) are n,nth roots of unity, then for k=1,2,3,…n

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  8. If z(1),z(2) and z(3), z(4) are two pairs of conjugate complex numbers...

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  9. If |z(1)|=|z(2)| and arg (z(1))+"arg"(z(2))=0, then

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  10. If one vertex of a square whose diagonals intersect at the origin is 3...

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  11. The value of z satisfying the equation logz+logz^2+dot+logz^n=0i s

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  12. If |z(1)|= |z(2)|= ….= |z(n)|=1, prove that |z(1) + z(2) + …+ z(n)|= |...

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  13. If omega is a cube root of unity and (1+omega)^7=A+Bomega then find th...

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  14. If omega(!=1) is a cube root of unity, then value of the determinant|1...

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  15. Let z and omega be two non-zero complex numbers, such that |z|=|omega|...

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  16. If z ne 0 be a complex number and "arg"(z)=pi//4, then

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  17. (1+i)^8+(1-i)^8=?

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  18. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

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  19. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

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  20. For any complex number z, the minimum value of |z|+|z-1|, is

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