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If z1a n dz2 are complex numbers and u=s...

If `z_1a n dz_2` are complex numbers and `u=sqrt(z_1z_2)` , then prove that `|z_1|+|z_2|=|(z_1+z_2)/2+u|+|(z_1+z_2)/2-u|`

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FIITJEE-COMPLEX NUMBER-ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - I
  1. (i) Let z be a non-real complex number lying on the circle |z|=1. Then...

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  2. (i) If 'a' is a complex number such that |a| = 1. Find the values of a...

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  3. If z1a n dz2 are complex numbers and u=sqrt(z1z2) , then prove that |z...

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  4. If z1, z2 are two complex numbers representing consecutive vertices of...

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  5. The vertices of a triangle in the argand plane are 3+4i, 4+3i and 2 sq...

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  6. If z= cos.(2pi)/(2n +1) +isin.(2pi)/(2n+1), n is a positive integer, t...

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  7. The minimum value of k for which |z-i|^2 + |z-1|^2 =k will represent a...

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  8. if (tanalpha-i(sin ""(alpha)/(2)+cos ""(alpha)/(2)))/(1+2 i sin ""(alp...

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  9. Assuming that log (mn) = log m + logn prove that log x^(n) = n log x, ...

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  10. Show that (1+x)^(n) - nx-1 is divisible by x^(2) for n gt N

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  11. Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is div...

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  12. If n gt 1 and x gt -1, x ne 0, show by the principal of mathematical i...

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  13. Show by using mathematical induction that n^(5) -n is multiple of 5.

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  14. Show that 5^(2n)+1 is divisible by 13 if n is odd. Hence show that 5^9...

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  15. 1.3+2.3^2+3.3^3+..............+n.3^n=((2n-1)3^(n+1)+3)/4

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  16. Show that 2^(2n) + 1 or 2^(2n)-1 is divisible by 5 according as n is o...

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  17. Show that 4.6^(n) +5^(n+1) leaves remainder 9 when divided by 20.

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  18. Show that the expression (n^5)/(5) + (n^3)/(3) + (7n)/(15) is a positi...

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  19. Show by mathematical induction that tan^(-1) .(1)/(3) + tan^(-1). (1)/...

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  20. Given a1=1/2(a0+A/(a0)), a2=1/2(a1+A/(a1)) and a(n+1)=1/2(an+A/(an)) ...

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