Complex Polynomial - Examples

Let's look at some examples of complex polynomials

• \(p(z) = 1\) is a complex polynomial with \(a_0=1\), and \(a_1= a_2=a_3=\cdots =0\). Therefore \(\Degree{p}=0\).
• \(p(z) = 2z-1\) is a complex polynomial with \(a_0=-1\), \(a_1=2\) and \(a_2= a_2=a_3=\cdots =0\). Therefore \(\Degree{p}=1\).
• \(p(z) = (1-i)z^2 + z+ 1+i\) is a complex polynomial with \(a_0=1+i\), \(a_1=1\), \(a_2 = 1-i\), and \(a_3= a_4=a_5=\cdots =0\). Therefore \(\Degree{p}=2\).
• \(q(z) = z^{16} - 1\) is a complex polynomial with \(a_0=-1\), \(a_{16}=1\) and \(a_k=0\) for \(k\neq 0,16\). Therefore \(\Degree{q}=16\).