## anonymous 5 years ago the area of the triangle formed by 1.w,w^2 in argand plane is? note that w means cube root of unity

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

2. 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 =$3/2\times \sqrt{3}/2\times2$ =$3\sqrt{3}/2$

3. anonymous

what is the formula for area of an equilateral triangle?