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

Complex Conjugate is the 849th xkcd comic.


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.

See alsoEdit

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