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If two nonzero complex numbers z1,z2 be ...

If two nonzero complex numbers `z_1,z_2` be such that `z_1+z_2` is real then they are necessarily conjugate to each other.

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If z is a nonreal compex number and |z|=1 then z^2+1/z^2=2 .

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  2. State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta)...

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  3. If two nonzero complex numbers z1,z2 be such that z1+z2 is real then t...

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  4. For complex numbersz1=x1+iy1" and " z2=x2+iy2 we write z1 cap z2 if x1...

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  5. If z is a nonzero complex number then (bar(z^-1))=(barz)^-1 .

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  6. If the points P and Q represent the complex numbers z and iz then angl...

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  7. If z1ne-z2 and |z1+z2|=|1/z1 + 1/z2| then :

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  8. Find z, if |(z+1)/(z+i)|=1

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  9. If in the Argand plane z1,z2,z3 and z4 are four points such that |z1|=...

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  10. State true or false: If zne0 then argz+argbarz=0.

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  11. Let z1 and z2 be the roots of z^2+pz+q=0. Then the points represented ...

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  12. If z1,z2 are nonzero complex numbers then |(z1)/(|z1|)+(z2)/(|z2|)|le2...

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  13. The nth roots of -1 can be n terms of a GP.

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  14. In the following, each question has one or more than one correct answe...

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  15. If |z-3i|=3 and amp z in (0, pi/2), then cot(amp z)-theta/z is eqaul ...

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  16. If zne0 then amp z +ampbarz = .

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  17. x+iy=((sqrt3+i)/(1-sqrt3i))^25 then x=, y=.

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  18. If alpha1,alpha2,alpha3,alpha4 be the roots of x^5-1=0 then prove that...

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  19. Consider the quadratic equation az^(2)+bz+c=0 where a,b,c and non-zero...

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  20. If |z^2-4|=2|z| then find the greatest value of |z|.

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