We studied in basic algebra under complex numbers that the nth roots of unity. 2kx 2...

 

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We studied in basic algebra under complex numbers that the nth roots of unity. 2kx 2² = 1 ⇒ z = (cos ( 24 ) :( cos( 2k² ) + i sin (2Kr)). / k = 0,1...n-1 n selects in equally spaced points on the unit circle. One implication of this is that if we find the cube roots of unity, we can create an equilateral triangle. Thus, One way to find an equilateral triangle on a unit circle centered at the origin is using the expression. 2kx (²Kr)), k=0.1.2 2³ = 1=z=(cos (cos (2k ² ) + i sin ( One way therefore to create an equilateral triangle with one vertex at an arbitrary point, is to translate the vertices above by the position vector of the arbitrary point. Which just amounts to addition of complex numbers. In [ ]: def unit_equilateral(n): # YOUR CODE HERE raise Not ImplementedError() Thus to get an equilateral triangle with one vertex at (2,3) we can find the cube root of unity and add the complex number 1 + 3i to each vertex since (1.0) is a vertex of the cube root of unity Create a function unit_equilateral(n) that takes as input a complex number and returns an equilateral triangle with one vertex centred at the point. Your code should return a list a list of 3 complex numbers where each element in the list is a vertex of the triangle. We studied in basic algebra under complex numbers that the nth roots of unity. 2kx 2² = 1 ⇒ z = (cos ( 24 ) :( cos( 2k² ) + i sin (2Kr)). / k = 0,1...n-1 n selects in equally spaced points on the unit circle. One implication of this is that if we find the cube roots of unity, we can create an equilateral triangle. Thus, One way to find an equilateral triangle on a unit circle centered at the origin is using the expression. 2kx (²Kr)), k=0.1.2 2³ = 1=z=(cos (cos (2k ² ) + i sin ( One way therefore to create an equilateral triangle with one vertex at an arbitrary point, is to translate the vertices above by the position vector of the arbitrary point. Which just amounts to addition of complex numbers. In [ ]: def unit_equilateral(n): # YOUR CODE HERE raise Not ImplementedError() Thus to get an equilateral triangle with one vertex at (2,3) we can find the cube root of unity and add the complex number 1 + 3i to each vertex since (1.0) is a vertex of the cube root of unity Create a function unit_equilateral(n) that takes as input a complex number and returns an equilateral triangle with one vertex centred at the point. Your code should return a list a list of 3 complex numbers where each element in the list is a vertex of the triangle.