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Let |(z(1) - 2z(2))//(2-z(1)z(2))|= 1 an...

Let `|(z_(1) - 2z_(2))//(2-z_(1)z_(2))|= 1` and `|z_(2)| ne 1`, where `z_(1)` and `z_(2)` are complex numbers. shown that `|z_(1)| = 2`

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To solve the problem, we start with the given equation: \[ \left| \frac{z_1 - 2z_2}{2 - z_1 z_2} \right| = 1 \] This implies that the modulus of the numerator is equal to the modulus of the denominator: ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. If alpha\ a n d\ beta are different complex numbers with |beta|=1,\ fi...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Prove that |Z-Z1|^2+|Z-Z2|^2=a will represent a real circle [with cent...

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  19. If |z-2-3i|^(2) + |z- 5 - 7i|^(2)= lambda respresents the equation ...

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  20. If (|2z - 3|)/(|z-i|)= k is the equation of circle with complex numbe...

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