User:AbyxDev/sandbox

User:abyxdev

function
/--> int factorial(int n)
| int return
| /--< (n > 0)
| | return = 1
| \-->
| /--< (n == 0)
| | return = (n * factorial((n - 1)))
| \-->
^ return

main
int n
print "Enter a number:"
n = (input int)
print "Factorial of", n, "is", factorial(n)

${\displaystyle {\begin{aligned}z_{1}&=R+R_{1}+iwL\\z_{2}&=R_{2}\\z_{3}&=R_{3}-{\frac {i}{wC_{3}}}\\z_{4}&=-{\frac {i}{wC_{4}}}\\\end{aligned}}}$

${\displaystyle {\begin{aligned}{\text{Substitute each term into }}{\frac {z_{1}}{z_{2}}}&={\frac {z_{3}}{z_{4}}}\\{\frac {R+R_{1}+iwL}{R_{2}}}&={\frac {R_{3}-{\frac {i}{wC_{3}}}}{-{\frac {i}{wC_{4}}}}}\\(R+R_{1}+iwL)\left(-{\frac {i}{wC_{4}}}\right)&=R_{2}(R_{3}-{\frac {i}{wC_{3}}})\\-{\frac {R}{wC_{4}}}i-{\frac {R_{1}}{wC_{4}}}i-i^{2}{\frac {{\cancel {w}}L}{{\cancel {w}}C_{4}}}&=R_{2}R_{3}-{\frac {R_{2}}{wC_{3}}}i\\-{\frac {R+R_{1}}{wC_{4}}}i+{\frac {L}{C_{4}}}&=R_{2}R_{3}-{\frac {R_{2}}{wC_{3}}}i\\{\text{Real part:}}&\\{\frac {L}{C_{4}}}&=R_{2}R_{3}\\L&=R_{2}R_{3}C_{4}\\{\text{Imaginary part:}}&\\-{\frac {R+R_{1}}{{\cancel {w}}C_{4}}}&=-{\frac {R_{2}}{{\cancel {w}}C_{3}}}\\(R+R_{1})(C_{3})&=R_{2}C_{4}\\RC_{3}+R_{1}C_{3}&=R_{2}C_{4}\\RC_{3}&=R_{2}C_{4}-R_{1}C_{3}\\R&={\frac {R_{2}C_{4}-R_{1}C_{3}}{C_{3}}}\\&={\frac {R_{2}C_{4}}{C_{3}}}-R_{1}\\\end{aligned}}}$