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Complex Conjugate

Number 849
Date Jan. 19th 2011
Previous 3D
Next World According to Americans

Complex Conjugate is the 849th xkcd comic.

## ExplanationEdit

A wavefunction is a function used in quantum mechanics to describe the quantum state of particles.

A wavefunction uses complex numbers, which are numbers that can be written in the form $a+b\times i$ where $a$ and $b$ are real numbers (which means ordinary numbers), and $i$ is the imagniary unit, an imaginary number that has the property that $i^2$ (i squared) equals $-1$. For instance, $2+3i$ is a complex number.

The complex conjugate of a complex number $a+b\times i$ is $a-b\times i$. So for instance the complex conjugate of $2+3i$ is $2-3i$.

Let's try and multiply a complex number by its complex conjugate:<br /> $(a+b\times i)\times(a-b\times i) = a\times a - a\times b \times i + a \times b \times i - b \times b \times i \times i = a^2 + b^2$<br /> because $- a\times b \times i$ and $+ a \times b \times i$ cancel each other out and $i\times i = -1$ The end result $a^2 + b^2$ doesn't have an imaginary part anymore, which means that it's a real number. Conclusion: multiplying a complex number by its complex conjugate makes it real.

By multiplying the wavefunction by it's complex conjugate, the teacher makes it a real number from a mathematical standpoint, and uses the catchphrase "shit just got real" made popular by the movie Bad Boys II. This expression is supposed to mean that something dangerous and/or extreme is going on, which is why the teacher started by saying "Okay, anyone who's feeling like they can't handle the physics here should probably just leave now."

## Mouseover textEdit

"Fun fact: if you say this every time a professor does something to a complex-number equation that drops the imaginary part, they'll eventually move the class to another room and tell everyone else except you."

Overuse of a catchphrase (such as "Shit just got real") can be very annoying. Overuse of this particular catchphrase in a quantum physics class could get a person removed from that class. The mouseover text jokes about a non-confrontational way this could be accomplished.