Question

Simplify the expression (10 + 3i)(10 - 3i).​

Answer 1

`(a-b)(a+b)=a^2-b^2`

Therefore

`(10 + 3i)(10 - 3i)=100-9i^2`

Answer 2

109

Explanation:

`\textbf{Assuming}~ i ~\textbf{as the imaginary unit, where}~ i = √(-1)~ \textbf{and}~ i^2 = -1\\\\\textbf{Given that,}\\\\~~~(10+3i)(10-3i)\\\\=10^2 -(3i)^2~~~~~~~~~~;\textbf{Difference of two squares} ~a^2 -b^2 = (a+b)(a-b)\\\\=100-9i^2\\\\=100-9(-1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;{i^2 = -1}\\\\=100+9\\\\=109`