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If `z` is a complex number, then find the minimum value of `|z|+|z-1|+|2z-3|dot`

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To find the minimum value of the expression \( |z| + |z - 1| + |2z - 3| \), we can follow these steps: ### Step 1: Define the expression Let \( e = |z| + |z - 1| + |2z - 3| \). ### Step 2: Analyze the terms We need to find the minimum value of \( e \). We can rewrite the third term: \[ ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. Find the minimum value of |z-1| if ||z-3|-|z+1||=2.

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

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  15. If complex numbers z(1)z(2) and z(3) are such that |z(1)| = |z(2)| = |...

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  16. If the triangle fromed by complex numbers z(1), z(2) and z(3) is eq...

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  17. Show that the equation of a circle passings through the origin and...

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  18. The triangle formed by A(z(1)), B(z(2)) and C(z(3)) has its circumc...

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  19. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

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  20. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, the...

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