Where does Euler's Formula come from?

Euler's Formula is: eix = cos(x) + isin(x)

This identity comes from the Maclaurin expansion of the exponential function. The resulting maclaurin series is a power series in x with odd terms having a factor of i. Seperating the odd and even terms, the odd terms give isin(x) and the even terms give cos(x).

LK

Related Further Mathematics A Level answers

All answers ▸

How do you find the derivative of arcsinx?


Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)


Prove that "6^n + 9" is divisible by 5 for all natural numbers.


It is given that f(x) = 2sinhx+3coshx. Show that the curve y = f(x) has a stationary point at x =-½ ln(5) and find the value of y at this point. Solve the equation f(x) = 5, giving your answers exactly