GreenPrint said:Homework Statement
Hi,
I have just now come to the realization that tan(pi/2) is not infinity but complex infinity. I was wondering why and can't seem to find the answer. I was told all through high school that tan(pi/2)=infinity or undefined but not complex infinity.
Homework Equations
The Attempt at a Solution
Tan(pi/2) is equal to complex infinity because the tangent function is undefined at pi/2, meaning it has no real value. Instead, it approaches infinity in the complex plane.
Complex infinity is a concept in complex analysis that represents a point in the complex plane where a function approaches infinity. It is not a specific number, but rather a way of describing the behavior of a function at a certain point.
Complex infinity and infinity in real numbers are different because they represent different concepts. In real numbers, infinity is a value that is greater than any finite number. In complex numbers, infinity is a point in the complex plane where a function approaches infinity, rather than a specific value.
Other trigonometric functions that can equal complex infinity include Cot(pi/2), Sec(pi/2), and Csc(pi/2). These functions are undefined at pi/2 and approach infinity in the complex plane.
The concept of complex infinity is used in various fields of science, such as physics, engineering, and mathematics. It is particularly useful in complex analysis and the study of complex functions. In physics, it is used in the study of electric fields and the concept of complex power. In engineering, it is used in the analysis of alternating current circuits.