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If z=x+iy then show that |x|+|y|lesqrt2|...

If z=x+iy then show that `|x|+|y|lesqrt2|x+iy|.`

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CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(LONG ANSWER TYPE QUESTION )
  1. If x,y,b and real, z=x+iy and (z-i)/(z-1)=ib, show that, (x-(1)/(2))...

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  2. If x+iy=(2)/(3+cos theta+isin theta),"show that" " " 2x^(2)+2y^(2)=3x-...

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  3. If y=sqrt(x^(2)+6x+8), show that one value of sqrt(1+iy)+sqrt(1-iy)[i...

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  4. Factorise : x^(2)+y^(2)+z^(2)-xy-yz-zx

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  5. prove that , (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=27abc...

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

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

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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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  16. If z(1)^(2)+z(2)^(2)+z(3)^(2)-z(1)z(3)-z(1)z(2)-z(2)z(3)=0" ""prove th...

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  17. Solve bar(z)=iz^(2) (z being a complex number)

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  18. Solve : |z|+z=2+i (z being a complex number)

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  19. If z=x+iy then show that |x|+|y|lesqrt2|x+iy|.

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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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