Complex numbers is a prerequisite to quantum mechanics. Everything in quantum mechanics is calculated in terms of complex numbers, even though at the end of these calculations one must obtain an answer in terms of the real numbers to compare with experimental results, since complex numbers are not “real” and can’t be the values of measurements. The last article explains the beautiful relationship between complex numbers and the trigonometric functions, which you may appreciate better after reading “Euler’s formula” listed in “A crash course in calculus, the second part.”