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If z1, z2, z3 are complex numbers such t...

If `z_1, z_2, z_3` are complex numbers such that `absz_1 = absz_2 = absz_3 = abs(1/z_1 + 1/z_2+ 1/z_3) =1` then show that `abs(z_1 + z_2 + z_3) = 1`.

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AAKASH SERIES-COMPLEX NUMBERS-SOLVED EXAMPLES
  1. Simplifiy i^(2)+i^(4)+i^(6)+.....+(2n+1) terms

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  2. Show that the least positive integral value of n for which ((1+i)/(1 -...

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  3. If ((1+i)/(1 -i)) - ((1 - i)/(1 +i)) = x +iy find x and y .

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  4. Show that sum(n=1)^(25) (i^(n) + i^(n +1)) = i-1

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  5. Show that (2-i)/((1-2i)^(2)) and ((-2-11 i)/(25)) are conjugate to eac...

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  6. Find the real values of theta , such that (3 + 2i sin theta)/(1 - 2i s...

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  7. Find the real values of theta , such that (3 + 2i sin theta)/(1 - 2i s...

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  8. If (sqrt(3)i)^(100)=2^(99)(a+ib). Then shot that a^(2)+b^(2)=4

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  9. If z1, z2, z3 are complex numbers such that absz1 = absz2 = absz3 = ab...

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  10. Area of the triangle formed by the Argrand diagram formed by the compl...

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  11. If z(z), z(2) are two non-zero complex numbers satisfying |z(2)+z(2)|=...

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  12. If z = x + iy and if the point P in the argand plane represents z then...

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  13. If z = x + iy and if the point P in the argand plane represents z then...

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  14. Show that the locus of z = x + iy such that the amplitude of (z -1)/(z...

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  15. Reduce the complex numbers 3 + 4i, 3/2 (7 +i) (1+i), (2(i-18))/((1 + i...

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  16. If (z(3)-z(1))/(z(2)-z(1)) is a real number, show that the points repr...

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  17. Describe geometrically the following subsets of C : {z inC |z-1 + i|...

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  18. Describe geometrically the following subsets of C : {z in C |z +i|le...

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