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If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) =...

If arg `((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3`, then `|z_(1)|` equals to

A

`sqrt(26)`

B

`sqrt(10)`

C

`sqrt(3)`

D

`2sqrt(2)`

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The correct Answer is:
B
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|z_(1)|=|z_(2)| and arg((z_(1))/(z_(2)))=pi, then z_(1)+z_(2) is equal to

If z_(1)&z_(2) are two complex numbers & if arg (z_(1)+z_(2))/(z_(1)-z_(2))=(pi)/(2) but |z_(1)+z_(2)|!=|z_(1)-z_(2)| then the figure formed by the points represented by 0,z_(1),z_(2)&z_(1)+z_(2) is:

If arg((z_(1))/(z_(2)))=(pi)/(2), then find the value of |(z_(1)+z_(2))/(z_(1)-z_(2))|

arg((z_(1))/(z_(2)))=arg(z_(1))-arg(z_(2))

arg(z_(1)z_(2))=arg(z_(1))+arg(z_(2))

Let z_(1),z_(2) and z_(3) be three complex number such that |z_(1)-1|= |z_(2) - 1| = |z_(3) -1| and arg ((z_(3) - z_(1))/(z_(2) -z_(1))) = (pi)/(6) then prove that z_(2)^(3) + z_(3)^(3) + 1 = z_(2) + z_(3) + z_(2)z_(3) .

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
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  4. If omega is a complex cube root of unity, then the equation |z- omega|...

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  8. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

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  10. If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unit...

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  11. If z(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0...

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  12. The least positive integer n for which ((1+i)/(1-i))^n= 2/pi sin^-1 (...

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  13. The area of the triangle formed by the points representing -z,iz and z...

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  14. If z(0)=(1-i)/2, then the value of the product (1+z(0))(1+z(0)^(2))(1+...

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  16. If the points in the complex plane satisfy the equations log(5)(|z|+3)...

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  17. A complex number z with (Im)(z)=4 and a positive integer n be such tha...

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  18. If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z(1)|...

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  19. If z(1) and z(2) satisfy the equation 2|z+3|=|"Re"(z)| and arg(z+3)/(1...

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  20. If A=|z in C: z=x+ix-1 for all x in R} and |z| le |omega| for all z, o...

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