# 849: Complex Conjugate

## Explanation[edit]

This comic is a joke on the common phrase "Shit just got *real*", meaning that something has suddenly increased in difficulty so it is now a real challenge. Cueball is standing in front of a board delivering a lesson, and is about to multiply a wavefunction by its complex conjugate. In mathematics, a complex number has a real part (a) and an imaginary part (b*the imaginary unit). The number can be written as a+b*i*. The complex conjugate of a number (a+b*i*) is a–b*i*. When one multiplies a complex number and its conjugate, the result is (a+b*i*)(a–b*i*), which is a^{2}–(b*i*)^{2} = a^{2}–b^{2}*i*^{2}. The imaginary unit *i* is defined as "the square root of –1", hence *i*^{2}=–1.

This process yields a result of (a^{2}+b^{2}) that does not have an imaginary part, making it a *real* number, which is a play on the aforementioned phrase. Accordingly, Cueball dictates that the people who are not skilled enough should leave.

The title text states that if you joke about this every time it's applicable, that will be annoying enough that the class will ditch you and attempt to take place in another room.

## Transcript[edit]

- [Cueball is standing at a whiteboard covered in equations, one of which is the time dependent Schrodinger equation.]
- Cueball: Okay, anyone who's feeling like they can't handle the physics here should probably just leave now.

- Cueball: Because I'm multiplying the wavefunction by its complex conjugate.
- Cueball: That's right.

- [Dramatic zoom. It appears Cueball is writing on the side of the panel.]
- Cueball: Shit just got
*real*.

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# Discussion

Actually multiplying complex number (x + iy) by its complex conjugate (x - iy) does not "remove" imaginary part, but calculate square of absolute value of complex number, (x^2 + y^2). BTW. in quantum physics the wavefunction is complex valued, and its absolute value is probability density (a real valued function). --JakubNarebski (talk) 00:57, 18 December 2012 (UTC)

I got hit in the face with my complex conjugate and lost an eye. 108.162.238.114 (talk) *(please sign your comments with ~~~~)*

I procreated with my complex conjugate and lost myself. 108.162.216.114 19:44, 12 August 2014 (UTC)

(a+bi)*(a-bi)= a^2-b^2 not a^2+b^2 108.162.218.142 15:48, 24 June 2015 (UTC)

(a+b)*(a-b) = a^2 - b^2 . However (a+bi)*(a-bi) = a^2 + b^2 since i^2 = -1. 108.162.219.65 (talk) *(please sign your comments with ~~~~)*

I think that the moving to a title text is a joke about them kicking you out of the room 173.245.50.65 20:54, 1 May 2016 (UTC)