In any polynomial involving i, i.e.

$ c1*i^n+c2*i^{n-1}+...+c $

we can express the even powers of i as either 1 or -1. Thus, any polynomial in i can be expressed as

$ c1+c2*i $

where c1 and c2 are any real number constants. This also establishes the set {1, i} as a basis for C as a vector space over all real numbers.

More importantly for our class, euler's formula:

$ e^{i\pi}=\cos(\theta)+i*\sin(\theta) $

also

$ e^{-i\pi}=\cos(\theta)-i*\sin(\theta) $

Alumni Liaison

has a message for current ECE438 students.

Sean Hu, ECE PhD 2009