Use the Maclaurin Series for f(x) =e^x to answer the following questions:(a)Evaluate f(x) at x=iθand expand the first 8 terms of the series (n= 0 to n= 7). (b)Simplify the first 8 terms of the series...

Use the Maclaurin Series for f(x) =e^x to answer the following questions:(a)Evaluate f(x) at x=iθand expand the first 8 terms of the series (n= 0 to n= 7).

(b)Simplify the first 8 terms of the series and group together the real and imaginary parts of the series.

(c)Look for a pattern for the real part and imaginary part of the series and write the Maclaurin Series for e^x as the sum of a real series and an imaginary series.

(d)Using the sum of the real and imaginary series above write an identity for e^x