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Given the three numbers z1 z2 z3 show that these complex numbers are vertices of an equilateral triangle inscribed in a circle centered at the origin and radius r?
Wiki User
∙ 9y ago
You cannot show it in general since it need not be true!
Wiki User
∙ 9y ago
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Given the three numbers z1 z2 z3 show that these complex numbers are vertices of an equilateral triangle inscribed in a circle?
An equilateral triangle is always inscribed in a circle.This means that if you can prove that z1, z2 and z3 are the vertices of an equilateral triangle, they automatically lie on a circle subscribing it.Compute |z1-z2|, |z1-z3| and |z2-z3|. These need to be equal for z1, z2 and z3 to lie on an equilateral triangle. If not, they aren't lying on an equilateral triangle.for z=a+ib, |z| = (a^2+b^2)^(1/2).To find the center c of the circle, note that (z1-c)+(z2-c)+(z3-c) = 0, hence,c = (z1+z2+z3)/3.
What is the perimeter of a triangle with vertices located at (1 3) (2 6) and () 4) rounded to the nearest hundredth?
1.00
Can a prism have an odd number of vertices's?
No. Not can it have an odd number of vertices.
Does a pyramid always have an odd number of vertices?
No. A pyramid can have any number of vertices from 4 upwards.
Can a prism have odd number of vertices's?
no
What shows an equilateral triangle inscribed in a circle?
An equilateral triangle inscribed in a circle has three sides that are equal in length and three angles that are each 60 degrees. The center of the circle is also the intersection point of the triangle's perpendicular bisectors.
What 2 shapes have the same number of vertices?
An isosceles triangle and an equilateral triangle both have three vertices.
The center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle?
true
What is the name of a circle that lies outside of the triangle and passes through all vertices of the triangle?
The triangle that has all three vertices touching the circle is called an 'inscribed triangle.' The circle has no special name, only the polygon inscribed.
What are regular Platonic solids and their properties?
There are only 5 known regular Platonic solids and they and their properties are:- 1 Tetrahedron: (pyramid) 4 equilateral triangle faces, 6 edges and 4 vertices 2 Hexahedron (cube) 6 square faces, 12 edges and 8 vertices 3 Octahedron: 8 equilateral triangle faces, 12 edges and 6 vertices 4 Dodecahedron: 12 regular pentagon faces, 30 edges and 20 vertices 5 Icosahedron: 20 equilateral triangle faces, 30 edges and 12 vertices All of them can be inscribed inside a sphere.
How do you find point symmetry for an equilateral triangle?
An equilateral triangle has 3 lines of symmetry which perpendicularly bisects each of its vertices
How many vertices faces and edges does a equilateral triangle have?
A triangle has 3 vertices and three sides (edges). It has one face.
Given the three numbers z1 z2 z3 show that these complex numbers are vertices of an equilateral triangle inscribed in a circle?
An equilateral triangle is always inscribed in a circle.This means that if you can prove that z1, z2 and z3 are the vertices of an equilateral triangle, they automatically lie on a circle subscribing it.Compute |z1-z2|, |z1-z3| and |z2-z3|. These need to be equal for z1, z2 and z3 to lie on an equilateral triangle. If not, they aren't lying on an equilateral triangle.for z=a+ib, |z| = (a^2+b^2)^(1/2).To find the center c of the circle, note that (z1-c)+(z2-c)+(z3-c) = 0, hence,c = (z1+z2+z3)/3.
Which solid figure has 4 vertices?
Tetrahedron: 4 equilateral triangle faces and 4 vertices.
How many vertices in a scalene triangle?
3 vertices in a triangle, whether it is equilateral, isosceles or scalene; acute angled, right or obtuse.
How manyVertices does an equilateral triangle have?
3(All triangles have 3 vertices)
How many sides and vertices does an equilateral triangle have?
All triangles have 3 sides and 3 vertices.
