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Show that the area of the triangle on the Argand diagram formed by the complex number `z ,i za n dz+i z` is `1/2|z|^2`

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. Let A(z1) and (z2) represent two complex numbers on the complex plan...

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  2. Find the area of the triangle whose vertices in the Argand plane are i...

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

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  4. Find the area of the triangle whose vertices represent the three roots...

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  5. The complex numbers z1, z2 and the origin form an equilateral triangle...

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  6. Complex numbers z1 , z2, z3 are the vertices A, B, C respectively of ...

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  7. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

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  8. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

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  9. Complex numbers z1 , z2, z3 are the vertices A, B, C respectively of ...

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  10. The points representing cube roots of unity

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  11. z, w, w^2 are the vertices of an equilateral triangle in the Argand pl...

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  12. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

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  13. If two consecutive vertices of a regular hexagon be z and barz , find ...

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  14. If z1,z2 are two complex numbers representing two consecutive vertices...

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  15. If two vertices of an equilateral triangle are z1,z2 then find the com...

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  16. The equation zbarz+abarz+baraz+b=0, b in R represents circle, if

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  17. Prove that |z-z1|^2+|z-z2|^2 = k will represent a circle if |z1-z2|^2 ...

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  18. Find all circles which are orthogonal to |z|=1and|z-1|=4.

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  19. If z=4i-5 then |z| = and barz = .

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  20. If the conjugate of (x +iy) (1-2i) be 1+ i, then:

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