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If the roots of (z-1)^n=i(z+1)^n are plo...

If the roots of `(z-1)^n=i(z+1)^n` are plotted in ten Arg and plane, then prove that they are collinear.

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To prove that the roots of the equation \((z-1)^n = i(z+1)^n\) are collinear when plotted in the Argand plane, we can follow these steps: ### Step 1: Rewrite the given equation We start with the equation: \[ (z - 1)^n = i(z + 1)^n \] ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
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  5. Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...

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  6. In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2...

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  7. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

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  9. A(z1),B(z2),C(z3) are the vertices of he triangle A B C (in anticlockw...

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  10. If one of the vertices of the square circumscribing the circle abs(z-1...

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  11. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

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  13. Let z1, z2a n dz3 represent the vertices A ,B ,a n dC of the triangle ...

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  14. F a=cos(2pi//7)+isin(2pi//7) , then find the quadratic equation whose ...

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  15. If omega is an imaginary fifth root of unity, then find the value of l...

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  16. If 1, alpha(1), alpha(2), alpha(3),…….,alpha(s) are ninth roots of uni...

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  18. Find roots of the equation (z + 1)^(5) = (z - 1)^(5).

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  19. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...

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  20. Let 1, z(1),z(2),z(3),…., z(n-1) be the nth roots of unity. Then pro...

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