• anonymous
the area of the triangle formed by 1.w,w^2 in argand plane is? note that w means cube root of unity
  • Stacey Warren - Expert
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  • chestercat
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  • watchmath
Maybe not the best attempt. But first you can try to find the coordinate of w and w^2 in the complex plane. After that you can use the area of triangle by using determinant. See here:
  • anonymous
\[1=\cos2n \pi+isin2 \pi\] \[1^{1/3}=(\cos2n \pi+i \sin 2n \pi)^{1/3}\] \[=\cos (2n \pi/3)+i \sin (2n \pi/3)\] =\[1+i0=1,\] for n= 1 \[-1/2+i \sqrt{3}/2\] for n=2 \[-1/2 -i \sqrt{3}/2\]for n=3 coordinates of the points are; \[(1,0)(-1/2, \sqrt{3}/2)(-1/2, -\sqrt{3}/2)\] Area of triangle =\[3/2\times \sqrt{3}/2\times2\] =\[3\sqrt{3}/2\]
  • anonymous
what is the formula for area of an equilateral triangle?

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