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In the complex plane, the vertices of an...

In the complex plane, the vertices of an equlitateral triangle are represented by the complex numbers `z_(1),z_(2) and z_(3)` prove that,
`(1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0`

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CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(LONG ANSWER TYPE QUESTION )
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  4. Factorise : x^(2)+y^(2)+z^(2)-xy-yz-zx

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  8. Express each of the following expressions as the sum of two squares: (...

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  9. If a,b are real and a^(2)+b^(2)=1 then show that the equation (sqrt(1...

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  10. If z=x+iy and |z|=1, show that (z-1)/(z+1)(z!=-1) is a purely imaginar...

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  11. If z(1)and z(2) be any two non-zero complex numbers such that |z(1)+z(...

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  12. If alpha be the real positive cube root and beta,gamma be the complex ...

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  13. If arg""(z-1)/(z+1)=(pi)/(4), show that the locus of z in the complex ...

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  14. In the complex plane, the vertices of an equlitateral triangle are rep...

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  15. Show that the area of the triangle on the Argrand Diagram formed by th...

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  20. Let z=x+iy and omega=(1-iz)/(z-i). If |omega|=1 show the in the comple...

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