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The area of the triangle with vertices $z,iz\:\:and\:\:-iz$ is ?

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  • If $z=x+iy$, then the point represented by z is $(x,y)$
  • $i^2=-1$
  • $|z|=\sqrt{x^2+y^2}$
  • Area of the triangle with vertices $(x_1,y_1),\:(x_2,y_2)\:and\:(x_3,y_3)$ is given by $\large \frac{1}{2}$$\left|\begin {array}{ccc}x_1 & y_1 & 1\\x_2 & y_2 &1\\x_3 &y_3&1\end {array}\right|$
Let $z=x+iy$
Then the vertices of the triangle are given by
$A(z)=(x,y), \:\:B(iz)=(-y,x)\:\:and\:\:C(-z)=(y,-x)$
Area of $\Delta \:ABC=\large \frac{1}{2}$$\left|\begin {array}{ccc}x & y & 1\\-y & x &1\\y &-x&1\end {array}\right|$
answered Jul 4, 2013 by rvidyagovindarajan_1

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