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 ▸

Find the general solution to the differential equation; y'' + 4y' = 24x^2


Give the general solution of the second order ODE dy2/d2x - 4dy/dx + 3 = 0


Prove that ∑(1/(r^2 -1)) from r=2 to r=n is equal to (3n^2-n-2)/(4n(n+1)) for all natural numbers n>=2.


Find the GS to the following 2nd ODE: d^2y/dx^2 + 3(dy/dx) + 2 = 0