Question

the area of the triangle formed by 1.w,w^2 in argand plane is?
note that w means cube root of unity

Answer 1

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: http://people.richland.edu/james/lecture/m116/matrices/applications.html

Answer 2

\[1=\cos2n \pi+isin2 \pi\]
\[1^{1/3}=(\cos2n \pi+i \sin 2n \pi)^{1/3}\]
\[=\cos (2n \pi/3)+i \sin (2n \pi/3)\]
=\[1+i0=1,\] 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 =\[3/2\times \sqrt{3}/2\times2\]
=\[3\sqrt{3}/2\]

Answer 3

what is the formula for area of an equilateral triangle?