E1: Reset. With a ={1,0} the partial sum series converges to e = 2.718....
Shift a along the real axis and compare results with the simulation of the geometric series.
E2: Choose real(a) ≈ 2.5, with arbitrary imaginary part.
What happens with the sequence?
Why does the series converge, while the absolute value of its sequence increases for the first members?
E3: Compare the character of convergence to that of the complex geometric series. What is responsible for the unlimited convergence of the exponential?
E4: Shift a along the imaginary axis, starting at 0.
How does the limit change? What is its formula? r = const = 1 = 1 * (cosa + i sina) ➙ eiy = cosy + i siny
E5: Shift a parallel to the imaginary axis.
How does the limit change? What is its formula?r = const = ea = ereal(a) eim(a) = ereal(a) (cos(im(a) + i sin(im(a)) ➙ ex + iy = ex(cosy + i siny ) Express this in words.