Question

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

Answer 1

Answer:

109

Step-by-step explanation:

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

Answer 2

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

Therefore

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