Is this a variant of Euler's Formula? Understanding e^iy = cosy + isiny

In summary, Eulers Formula variant is a mathematical formula that relates the number of faces, vertices, and edges of a polyhedron. It is an extension of Euler's formula and is significant in understanding the relationship between these elements in a polyhedron. It is derived from the original Euler's formula and has the formula V - E + F = H + 2. Eulers Formula variant is commonly used in mathematics, particularly in the fields of geometry, topology, and graph theory, as well as in computer graphics, engineering, and physics.
  • #1
SpartanG345
70
1
Eulers formula says that e^ix = cosx + isinx

but in my textbook there's another formula its e^ikx = coskx + isinkx
i still can't figure out how they got that. Is this still eulers formula? and how do u get it in that form
 
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  • #2
e^iy = cosy + isiny

Let y = kx

e^ikx = coskx + isinkx
 

What is Eulers Formula variant?

Eulers Formula variant is a mathematical formula that relates the number of faces, vertices, and edges of a polyhedron. It is an extension of Euler's formula, which applies to simpler shapes such as triangles, rectangles, and circles.

What is the significance of Eulers Formula variant?

Eulers Formula variant is significant because it helps us understand the relationship between the number of faces, vertices, and edges in a polyhedron. It also has applications in geometry, topology, and graph theory.

How is Eulers Formula variant derived?

Eulers Formula variant is derived from the original Euler's formula, which states that the number of faces plus the number of vertices minus the number of edges equals 2. The variant takes into account the number of holes or handles in a polyhedron, and adds an extra term to the formula.

What is the formula for Eulers Formula variant?

The formula for Eulers Formula variant is V - E + F = H + 2, where V is the number of vertices, E is the number of edges, F is the number of faces, and H is the number of holes or handles in a polyhedron.

In what fields is Eulers Formula variant commonly used?

Eulers Formula variant is commonly used in mathematics, specifically in the fields of geometry, topology, and graph theory. It also has applications in computer graphics, engineering, and physics.

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