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If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z...

If `|z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 ,` then find the value of `|z_1+z_2+z_3|dot`

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To solve the problem, we need to find the value of \(|z_1 + z_2 + z_3|\) given the magnitudes of the complex numbers and a specific condition. ### Step-by-Step Solution: 1. **Given Information**: - \(|z_1| = 1\) - \(|z_2| = 2\) - \(|z_3| = 3\) ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

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  2. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)+.......

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  3. If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z3+z2z3|=12 , then find the val...

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  4. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

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  5. Given that |z1+z2|^2=|z1|^2+|z2|^2, prove that z1/z2 is purely imagina...

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  6. Let |(z(1) - 2z(2))//(2-z(1)z(2))|= 1 and |z(2)| ne 1, where z(1) and...

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  7. If z1a n dz2 are two complex numbers and c >0 , then prove that |z1+z2...

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  8. If z1, z2, z3, z4 are the affixes of four point in the Argand plane, z...

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  9. if |z1+z2|=|z1|+|z2|, then prove that a r g(z1)=a r g(z2) if |z1-z2|=...

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  10. Show that the area of the triangle on the Argand diagram formed by the...

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  11. Find the minimum value of |z-1| if ||z-3|-|z+1||=2.

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  12. Find the greatest and the least value of |z1+z2| ifz1=24+7ia n d|z2|=6...

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  13. If z is a complex number, then find the minimum value of |z|+|z-1|+|2z...

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  14. If |z1-1|lt=,|z2-2|lt=2,|z(33)|lt=3, then find the greatest value of |...

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  15. Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (...

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  16. Identify the locus of z if z = a +(r^2)/(z-a),> 0.

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  17. If z is any complex number such that |3z-2|+|3z+2|=4 , then identify t...

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  18. If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus o...

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  19. Let z be a complex number having the argument theta ,0 < theta < pi/2,...

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  20. How many solutions the system of equations ||z + 4 |-|z-3i|| =5 and...

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