A complex number is a number that contains both a real part and an imaginary part. It can be written in the form a+bi, where a is the real part and bi is the imaginary part (with i representing the square root of -1).
The power of a complex number is the result of raising that number to a certain exponent. This is done by using the same rules as for real numbers, with the added consideration of the imaginary unit i.
To calculate the power of a complex number, you can use the polar form or the rectangular form of the number. In both cases, you can use the De Moivre's theorem to simplify the calculation.
Complex numbers have many applications in science, including in physics, engineering, and mathematics. They are used to describe and analyze phenomena that involve oscillations, such as waves and electricity, and are also used in the study of quantum mechanics and signal processing.
Yes, a complex number can have a negative power. This is because complex numbers have both a real and imaginary part, and raising a complex number to a negative power will result in a reciprocal of the original number. However, the result may be a complex number with a different magnitude and angle.