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Let C and R denote the set of all com...

Let `C` and `R` denote the set of all complex numbers and all real numbers respectively. Then show that `f: C->R` given by `f(z)=|z|` for all `z in C` is neither one-one nor onto.

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ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Single Option Correct Type Questions)
  1. If f(x)=g(x^(3))+xh(x^(3)) is divisiblel by x^(2)+x+1, then

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  2. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

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  3. Let C and R denote the set of all complex numbers and all real numb...

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  4. Let alpha and beta be two distinct complex numbers, such that abs(alph...

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  5. The complex number z satisfies thc condition |z-25/z|=24. The maximum ...

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  6. The points A,B and C represent the complex numbers z(1),z(2),(1-i)z(1)...

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  7. Find the 6th term of A.P if a=1 , d=2

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  8. Find the 3rd term of A.P if a=1 , d=2

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  9. The centre of circle represented by |z + 1| = 2 |z - 1| in the complex...

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  10. If x=9^(1/3) 9^(1/9) 9^(1/27) ......and if y= 4^(1/3) 4^(-1/9) 4^(1/...

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  11. Find the 5th term of A.P if a=1 , d=2

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  12. Let |Z(r) - r| le r, Aar = 1,2,3….,n. Then |sum(r=1)^(n)z(r)| is less ...

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

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  14. Find the 7th term of A.P if a=1 , d=2

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  15. Find the 10th term of A.P if a=1 , d=2

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  16. If z=(3+7i)(lambda+imu)," when " lambda,mu in I-{0} " and " i=sqrt(-1...

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  17. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

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  18. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

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  19. If m and n are the smallest positive integers satisfying the relation ...

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  20. Number of imaginergy complex numbers satisfying the equation, z^(2)=ba...

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