A complex number angle is a measure of rotation or direction in the complex plane. It is represented by the argument of a complex number, which is the angle between the positive real axis and the vector representing the complex number.
The angle of a complex number can be found by taking the inverse tangent of the imaginary part divided by the real part. This can be represented as θ = tan-1(Im(z)/Re(z)), where z is the complex number and θ is the angle in radians.
Yes, the angle of a complex number can be negative. A negative angle indicates a rotation in the clockwise direction, while a positive angle indicates a rotation in the counterclockwise direction.
The range of complex number angles is from -π to π radians. This is because the complex number plane is circular, and one full rotation corresponds to 2π radians. Therefore, any angle outside of this range can be simplified to an equivalent angle within this range.
Complex number angles are used in various fields of mathematics and science, including physics, engineering, and signal processing. They are particularly useful in analyzing and solving problems involving oscillatory functions, such as waves and vibrations, as well as in representing and manipulating complex numbers in polar form.