What is Complex Number?

The number $a$ is the real part and $b$ is the imaginary part. Complex numbers are added and multiplied like expressions in $i$, using $i^2 = -1$. The modulus is $|z| = \sqrt{a^2 + b^2}$ and the conjugate of $a + bi$ is $a - bi$. They let every quadratic equation have a solution: $x^2 + 1 = 0$ gives $x = \pm i$. Complex numbers are used in electrical circuits and in waves.