Question

Find the NORMALIZED Gaussian factorization of -14+102i

Polynomial factorization
ANSWERED
asked 2021-05-07
Find the NORMALIZED Gaussian factorization of -14+102i

Answers (1)

2021-05-08
-14+102i
\(N(a+bi)=(a+bi)(a-bi)=a^{2}+b^{2}\)
N(-14+102i)=(-14+102i)(-14-102i)
\(=(-14)^{2}+(102)^{2}\)
=10600
Then, the prime factorization becomes
\(10600 = 2\times 2\times 2\times 5\times 5\times 53\)
\(=[(1+i)(1-i)]^{3}[(1+2i)(1-2i)]^{2}(7+2i)(7-2i)\)
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