- #1
Khan
I'm having some problems expanding i^i, could anyone help? I know it becomes a real number somehow, and I'm familiar with the e^(i * pi) expansion, but is the i^i done in the same way?
A Taylor series for i^i is a mathematical series that represents the value of i^i, where i is the imaginary unit.
A Taylor series for i^i is derived by using the Taylor series expansion formula, which calculates the value of a function at a given point by using the function's derivatives at that point.
The first few terms of the Taylor series for i^i are: i^i = 1 + i(ln(i)) - 1/2(ln(i))^2 - 1/6(i)(ln(i))^3 + 1/24(i)(ln(i))^4 + ...
The accuracy of the Taylor series for i^i depends on the number of terms used. The more terms used, the closer the approximation will be to the actual value of i^i.
The Taylor series for i^i is used in various fields of mathematics and physics, such as complex analysis and quantum mechanics, to approximate the value of i^i and make calculations more manageable.