What complex numbers are and what they are used for.
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Complex numbers are often presented as “a real number & an imaginary number”. However, this is not IME the representation that truly capture what complex numbers means. There is a mathematically equivalent representation of complex numbers which is
**Complex number = Real number & Angle**, where every 180° in the angle means multiplying by -1.
As such, a complex number can be seen as “you were in the middle of changing a +3 into a -3, but you stopped at the middle of changing the sign so you’re in between positive and negative”. Said otherwise, the angle can be seen as representing a rotation or an oscillation of some sort.
It means that complex numbers find use everywhere there is some rotation or oscillation. In electricity, alternative current oscillate => complex numbers are used to represent the current. In quantum mechanics, you will often use both an amplitude (the real number) and a phase (the angle).
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