Complex Numbers

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined by i² = -1.
Complex numbers can be added, subtracted, multiplied, and divided using the rules of algebra.
The modulus of a complex number is the distance from the origin to the point in the complex plane that represents the number.
The amplitude of a complex number is the angle that the line from the origin to the point in the complex plane that represents the number makes with the positive real axis.
The conjugate of a complex number is obtained by changing the sign of the imaginary part.

\( z=a+bi \), where \( a,b\in\mathbb{R} \) and \( i^2=-1 \).
\( |z|=\sqrt{a^2+b^2} \) is the modulus of the complex number.
\( \text{Arg}(z)=\theta \), where \( \theta \) is the argument of the complex number, i.e. the angle it makes with the positive real axis in the complex plane.
\( \text{Re}(z)=a \) and \( \text{Im}(z)=b \) are the real and imaginary parts of the complex number, respectively.
\( \overline{z}=a-bi \) is the complex conjugate