- #1
mkbh_10
- 222
- 0
Homework Statement
Find the real & imaginary parts of log(1+i)log(i) ?
mkbh_10 said:= i pi log(2)-(pi)^2/8
tell me how to get these mathematical symbols , how to write an eqn like you have written ?
mkbh_10 said:Its not working like that
tiny-tim said:… if neither of these work, I'll start a thread in the Lounge section to see if anyone else knows what to do!
The real part of a logarithm is the number that is raised to a certain power to get the given logarithm. For example, in log(base 10) 100, the real part is 10. The imaginary part of a logarithm is a number that, when added to the real part, would make the given logarithm equal to 0. For example, in log(base 10) 100, the imaginary part is 0.
Logarithms have both real and imaginary parts because they are complex numbers, meaning they have both a real and imaginary component. This allows for a more complete representation of the number and allows for certain operations, such as exponentiation, to be performed more easily.
The real and imaginary parts of logarithms can be calculated using the properties of logarithms and complex numbers. For example, the real part of a logarithm can be found by taking the logarithm of the absolute value of the number, and the imaginary part can be found by taking the argument (angle) of the complex number.
The imaginary part of logarithms is significant because it allows for the representation of complex numbers, which are used in many areas of mathematics and science. Additionally, the imaginary part can provide information about the behavior and properties of the logarithm, such as its periodicity and the presence of singularities.
Logarithms with imaginary parts are used in a variety of practical applications, such as in signal processing, electrical engineering, and quantum mechanics. They are also used in the study of complex systems, such as chaos theory and fractal geometry. In these applications, the imaginary part of logarithms provides important insights and understanding into the behavior of complex systems and phenomena.