Question

1. The period of f(Z)=e* is​

Answer 1

Answer:

Recall the definition: if θ ∈ R then

e

iθ def = cos θ + isin θ. Clearly e

i(θ+2π) = e

iθ (because of the 2π periodicity of the sine and

cosine functions of ordinary calculus). It’s also clear—from drawing a picture of e

iθ on the

unit circle, say—that 2π is the “minimal period” of the imaginary exponential, in the sense

that if a ∈ R has the property that e

i(θ+a) = e

iθ for every θ ∈ R then a = 2πn for some

integer n.

II. Periodicity of complex the exponential. Recall the definition: if z = x + iy where