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If z(1)=1+isqrt3and z(2)=sqrt3-i, show t...

If `z_(1)=1+isqrt3and z_(2)=sqrt3-i,` show that
`arg(z_(1)z_(2))=argz_(1)+argz_(2)`

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CHHAYA PUBLICATION-COMPLEX NUMBER-EXERCISE 4(LONG ANSWER TYPE QUESTION )
  1. If z(1)=1+isqrt3and z(2)=sqrt3-i, show that arg(z(1)z(2))=argz(1)+ar...

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  2. If z(1)=1+isqrt3and z(2)=sqrt3-i, show that arg""(z(1))/(z(2))=argz(...

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  3. If |z(1)|=|z(2)|and argz(1)+argz(2)=0, then show that z(1) and z(2) ar...

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  4. If |z(1)|=|z(2)|=1 and argz(1)+argz(2)=0 then show that z(1)=1

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  5. If |z(1)|=|z(2)|and argz(1)~argz(2)=pi, "show that" " " z(1)+z(2)=0.

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  6. If z(1)=(sqrt3-1)+(sqrt3+1)i and z(2)=-sqrt3+i" ""find" " "arg z(1) an...

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  7. Find the values of x and y (real) for which the following equation is ...

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  8. If x,y,b and real, z=x+iy and (z-i)/(z-1)=ib, show that, (x-(1)/(2))...

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

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

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

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

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

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

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

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

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

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

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

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

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