Thanks for pointing that out.DrClaude said:There is a FAQ on the subject: https://www.physicsforums.com/showthread.php?t=637214
When we raise a number to an imaginary power, we are essentially multiplying that number by itself a certain number of times, where the number of times is represented by the imaginary unit, i. This results in a complex number with a real and imaginary component.
λi and e^lnx are both examples of raising a number to an imaginary power, but they have different bases. λi raises the number lambda (λ) to the power of the imaginary unit, i, while e^lnx raises the number e (the base of the natural logarithm) to the power of ln(x), the natural logarithm of x.
Imaginary powers are important in mathematics because they allow us to solve equations and problems that cannot be solved using only real numbers. They also have various applications in fields such as physics, engineering, and finance.
Yes, we can raise any number to an imaginary power. This will result in a complex number, unless the exponent is an integer multiple of π, in which case the result will be a real number.
To calculate a number raised to an imaginary power, we can use a mathematical formula called De Moivre's formula, which involves converting the number to polar form and using trigonometric functions. Another method is to use the properties of complex numbers, such as the distributive and associative properties, to simplify the expression and then solve it using basic arithmetic.