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Numbers of the form $\{z= x+ i\,y:\;x,\, y\in\mathbb{R}\}$ where $i^2 = -1$. Useful especially as quantum mechanics, where system states take complex vector values.
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Example on Snell's Law with complex solution
Snell's Law:
$$\frac{\sin(\theta_1)}{\sin(\theta_2)}=\frac{n_2}{n_1}$$
I have read some explanation on understanding complex Snell's Law like Explanation of sin(theta) > 1 for total internal reflectio …