Complex Conjugate | |
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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 <math>a+b\times i</math> where <math>a</math> and <math>b</math> are real numbers (which means ordinary numbers), and <math>i</math> is the imagniary unit, an imaginary number that has the property that <math>i^2</math> (i squared) equals <math>-1</math>. For instance, <math>2+3i</math> is a complex number.

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

Let's try and multiply a complex number by its complex conjugate:<br /> <math>(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</math><br /> because <math>- a\times b \times i</math> and <math>+ a \times b \times i</math> cancel each other out and <math>i\times i = -1</math> The end result <math>a^2 + b^2</math> 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.