# Why does the complex conjugate of psi pop out?

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1. Nov 2, 2015

### Indianspirit

I just started teaching myself multivariable calculus and I know what the modulus of a complex number is but what is the complex conjugate and why does it pop out when we take the mod square of psi?

Like the first minute or two of video...

What are complex conjugates, how does one find them, etc...

2. Nov 2, 2015

### andrewkirk

The conjugate of a complex number is what you get when you reverse the sign of the imaginary part of the number.
That is, the complex conjugate of $a+bi$ is $a-bi$.
It is usually denoted by an asterisk, as in $(a+bi)^*=a-bi$.
Complex conjugates have some neat properties, including that $(z1+z2)^*=z1^*+z2^*;\ (z1\ z2)^*=z1^*\ z2^*$.
Also, $z+z^*$ is real and equal to double the real part of $z$.
Geometrically in the Argand diagram, the complex conjugate of a number is its reflection in the real axis.

3. Nov 2, 2015

### Staff: Mentor

What do you mean by "pop out"?

4. Nov 3, 2015

### ddd123

I think he means this: $$\Psi^* \Psi = |\Psi|^2$$
which can be deduced easily from the properties in andrewkirk's post.