It Can Be Shown That the Maclaurin Series For $e^{z}$ $\cos z$

Essay

It can be shown that the Maclaurin series for $e^{z}$ , $\cos z$ and $\sin z$ converge for all values of z in the complex numbers, just as they do for all values of x in the real numbers.
a)Write down and simplify the Maclaurin series for $e^{i x}$ .
b)Write down the Maclaurin series for $\cos x$ and $i \sin x$ c)Use the series you found in parts a)and b)to show that $e^{i x}=\cos x+i \sin x$ .(This is one of several formulas called "Euler's Formula.")
d)Find the value of $7\left(e^{i s}+1\right)$ .