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Show that the area of the triangle on th...

Show that the area of the triangle on the Argand diagram formed by the complex numbers z, zi and `z+ zi` is `=(1)/(2) |z|^(2)`

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The correct Answer is:
Area of ` Delta OAB = 1/2 OA xx OB = 1/2 |z||iz| = 1/2 |z|^(2)`
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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. Prove that the complex numbers z(1),z(2) and the origin form an equ...

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  2. If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...

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  3. Show that the area of the triangle on the Argand diagram formed by the...

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  4. Complex numbers z(1),z(2)andz(3) are the vertices A,B,C respectivelt o...

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  5. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

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  6. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

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  7. Find the non-zero complex number z satisfying z =i z^2dot

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  8. Let z1 \and\ z2 be the roots of the equation z^2+p z+q=0, where the co...

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  9. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

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  10. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

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  11. about to only mathematics

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  12. Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...

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  13. Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...

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  14. If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5, then (a)...

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  15. Let (-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=sqrt(-1)), where x and y are re...

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  16. Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) T...

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  17. If (x-alpha)/(z+alpha)(alpha in R) is a purely imaginery number and |z...

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  18. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

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  19. if z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) ), then ( 1 + ...

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  20. All the points in the set S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt...

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